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ALL CLASSES: I may collect hwk assignments unannounced; if you have < 5 probs, I will grade all of them (no partial credit); if >5, I will randomized what probs to check..this will give us additional assignment grades.
3/18–Mr. Goldstein’s handout: pg. 79: 43, 44 also: textbook: pg. 596: 42, 48, 49, 52 (assigned 3/13); pg. 604: 35-41 (Root -ready made for root test)
3/15–pg. 603: 15-33, multiples of 3
3/13–pg. 595; 30-32, 42, 48, 49, 52 . We will have a minor assignment (test?) either tomorrow or Friday on testing a series for convergence based on all the tests we have discussed so far (you will find a nice summary on pg. 602). Please note that the root and ratio tests will not be included since we have not discussed them yet (they are in a class by themselves). 0on te
3/12–pg. 595: 9-26, multiples of 3; 26, 29
3/11- Euler’ method (start with a given point, use dy/dx (given in problem or obtained by differentiating f(x)), use given Δ x, obtain Δy , then new point is
(x + Δx, y + Δy), then continue the algorithm as required by the problem Homework 10, 13, 14–DO ONLY N=4 (that is, four iterations!!), otherwise you will be up all night…redundant! of course, you can code a program to do this, if you wish…Mr. Williams and I will be impressed!) In short, you are getting a bunch of tangent lines (linearizations) Δy = (dy/dx) (Δx)
2/27– pg. 587: 29-36
2/26–pg. 587: 4-14 (even–direct comparison); 16-26 (even–LCT)
2/22–pg. 582: 53-64, all
2/21–pg. 580: 1-8
2/20–Test–major assignment to cover all topics discussed since the beginning of the new year (arc length, improper integrals, L’Hopital’s, comparison test for series, telescoping series, geometric series, integration by parts and partial fractions) + some AB topics discussed in class (Reimann sums, FTC, etc).
2/19–Read 8.3–we will have either a participation grade or minor assignment tomorrow–review telescoping and geometric series as well as comparison test. Any lingering questions from the hwk assigned on 2/7- 2/18?
2/18–pg. 573: 27-45
2/15-pg. 573: -7-16
2/14–pg 573; 1-6; 21-22
2/7–pg. 564: 27-30; 37-42
2/1–Graded your assignment from 1/28–logistic functions. We need to have a discussion about grades and assignments, particularly class participation–we need to get more grades. Homework: pg. 548–47-56, 69, 70…do you have any questions about any probs assigned last week?
1/31–pg. 547; 32,43,42
1/30–pg. 547 15-25, odd (any lingering questions from 1/29?)
1/29–pg. 547: 1-13, odd
1/28–Read 7.8, ‘Improper Integrals” — pay attention to examples and different scenarios (Carter Nugent’s favorite word) that may arise.1/24–Handout, 17; Assessment grade tomorrow.
1/23–Handout: 1-4, 9,13
1/17–pg. 523–56, 58
1/16–pg. 522: 7-14, 29, 30, 41, 51, 52
1/14–pg.447: 9, 10 (Haseeb only, why?), 16, 17; pg. 495, 97 (omit “c”).
1/11–pg. 494: 37, 40, 41, 42 43, 44 (print from www. mathgraphs.com), 53, 56, 59-64. Use LIPET and/or tabular method if you wish where appropriate.
1/10–pg. 494: 2-36, even (Use LIPET whenever possible to help)
1/9–Read 7.2–There are some excellent videos on line (Youtube) that explain the approach patiently and diligently as well as giving hints.
3/19– photocopied pg. 384; 24, 25, 31-40
3/18–pg. 432: 5-10; 23, 24, 31- 36 (use half angle formulas, exact answers only).
3/15–pg. 475: 1-9, 11, 15, 19
3/14–pg. 374–33-38; pg. 378: 25
3/13–pg 373 (photocopied, old book) : 1-10; 17, 19, 26, 28, 30
3/12–Read 5.3; we will derive cos (u +v), sin (u + v) , sin (u-v) and (if we have time), tan (u+v) tomorrow.
3/11–Photocopied page (Alex, you are a popular person) 25-30
2/27–pg. 326: photocopied (old book)–1-19, even.
2/26–Handout: 12, 28, 29, 39 (back)
2/25–pg. 306: 19-26, all
2/21–pp 418-419: 23, 42, 48, 49, 51 (the last four involve algebraic manipulation); Extra for experts: (Bakta?) 70
2/20–photocopied page 321; 13-24 .
2/19–9-16, pg. 410
2/15–Test on Monday, 2/18
2/14–pg. 401: 99, 100, 106 (calculator needed–hint: what is the height when ‘The Beast” hit the ground? We are solving for x, the horizontal distance..look at the formula, what does x represent?). Read 5.1
2/13–We need to practice on problems involving applications of right triangles; we have not spent too much time on the topic and we will include it on your next major assignment (either Fri or Monday, probably the latter)..so do 94-98, pg. 401
2/10–Be prepared for a major assignment on Monday (definitely on Tuesday); if we don’t have a test on Monday, then we will continue to investigate graphing such as a “damped”factor ex: 2^x (sin x), and further applications.
2/7–pg. 366; 16-28
2/6–pg. 358: 72-76 (75 done in class)
2/5–pg. 358 (3+5 = 8, how cool is that? , easy to remember only Ryan and I would think of stuff like that) 60, 61, 68 ( graph the last two), 75.
2/1–Read (or google) transformations of trigonometric graphs (also called sinusoids). Pay attention to amplitude, vertical/horizontal shifts, and period. I have handouts for you that outline process clearer than your textbook. Experiment with your graphing calculator.
1/31–Test tomorrow DOK 1..study your graphs, quadrants, formulas (definition of radians, converting from degrees to radians and viceversa, area of a sector, length of an arc, apparent size), inverse functions, etc.
1/30–Will go over your minor assignment in class, study guide assigned for homework as well as probs assigned on 1/29 that we did not address this morning. Please note: I expect you to ask questions in class and do your homework–according to your grades you are not doing what is expected, so, let’s be proactive (that means, “get cracking”, do what is expected).
1/29–Minor assignment tomorrow–review your quadrants, reference angles, unit circle, graphs of trig functions (inverse functions are not included on this assessment). You won’t have to graph any of the trig functions, but you have to be familiar with characteristics of graphs such as asymptotes, even/odd, domain and range, continuity, etc. HWK; pg. 385: 23-32, 44-46
1/28–Read 4.7 (again, now that the section has been explained reinforce what you have learned). pg. 385: 1-12
1/25–Read 4.7–I have a special handout for you on Monday. Focus on the most common inverse trig functions: sin¯¹ (x), cos ‾¹ (x), and tan ‾¹ (x). In some books inverse trig functions are referred to as (Arcsine, Arccos, and Arctan–mainly in older math books, if you come across this notation, don’t panic-you are being asked to find the inverse). Relate the inverses to the the graphs of the original functions. Please note: the answer to an inverse trig function is an angle, however we don’t go around the whole circle since inverse trig functions are restricted. On Monday we will have a minor assessment grade on Monday (no graphing included).
1/23–Keep up with your notes as a pop quiz may happen at any time (may be a class participation grade or a minor assignment, depending on the length and difficulty). What did we learn today? How to graph the sine and cosine functions as well as their characteristics (pp. 350 and 351 in your text, although you can always google the material and see how it is done). For hwk (Alex, before your dream interlude) pg. 286 (old book) 15-18. Your best friend: the unit circle, therein lie all the answers (Think of it as “the Holy Grail of trigonometry” :)
1/22–pg. 348: 67-70; pg. 366: 29-34 –Jieni Chen should be satisfied that the hwk was posted at 9:50 AM (thank you for keeping me on my toes!)
1/18–Please do the hwk for 1/17 if you haven’t done it (posted too late); for Tues 1/22: pg. 335: 53, 56, 61, 62; pg. 394–8, 16
1/17–pg. 348: 43-48
1/16–pg. 347–finish 37; pg. 335 (right triangle trigonometry)–1, 4,7,9 (what do you notice about the measures given? Look up “Pythagorean triples”). Also, look up “reference angle” or “reference triangle”.
1/15–pg. 347–13-42 (exact answers only..may use handouts as a guide, since you are learning; will be delighted if you could do this without assistance
1/14–pg. 325: 35, 36 (Kiet), 38 (Noah), 56 (Yves, c’est la question qu tu m’a pose apres la classe; alors, je crois que tu pourrais le expliquer)
pg. 347: 1-5, 9, 10
1/11–pg. 265: 11,12; pg. 266–18, 19, 20
1/10–Phtocopied pg. 265 (old book, 3-10)
1/09– pg. 325, text–you may use a calculator, although not needed (1-8). Read 4.1 so that you can be prepared for tomorrow. Any time you have a reading assignment, pay attention to formulas and the main ideas/concepts (highlighted in blue rectangles), new vocabulary (boldface) as well as the marginal notes (annotations)…Every section begins with “What you will learn about” followed by “why”..(I will not repeat this info going forward)., pay attention to examples (in this case, exs. 1, 2, and 3).
12/13–Textbook: Read 5.6–pay attn highlighted rectangles. Notice that if we have SAS or SSS given we use the Law of Cosines (LOC). We use SAS to find the side opposite the known angle; we use SSS if we want to find any of the angles opposite any of the three given (known) sides, in which case we manipulate the formula as Logan pointed out this morning. Become familiar with Hero’s formula (cool to know), although I won’t ask you for its derivation (it is based on the LOC)..so, if given three sides of a triangle, we can find the area (provided the measures given determine a side). HOMEWORK: PG. 448 10, 22, 26, 30, 32, 38, 40**
12/12–Photocopied pg. 348: 8, 18, 19, 21, 22
12/11–Use the Law of Sines: pg. 439–6, 20, 27, 40
12/10–How do we find the area of a triangle given two sides and the included angle (SAS)? A = ½ (side 1) (side 2) (sine included angle). Now, for your homework:
Photocopied pp 343-43: 3, 8, 10, 12, 19, 20
12/7–photocopied pg.336: 21, 22, 23
12/6–Phtocopied pg. 335 13-20
12/3– The half angle formulas are derived from the cos 2Θ, –pg. 432 (text) 31-36; 43-46. In +, photocopied page (see below): 11- 18, 23
11/30–HW– (photocopied pages, old book) pp. 383-384-Written Ex 2-10, 19, 20, 22, 32, 33, 39
11/29–It is the season to check homework! HW–pg. 432 (Thank you, Logan): 5-9, 12, 15-17, 19, 21. This morning we derived the double angle formulas based on the + formulas. In summary:
sin 2x= sin (x+x)= sin x cos x +sin x cos x = 2 sinxcosx.
cos 2x = cos x cos x – sin x sin x = cos²x – sin²x (may be written as 2cos²x-1 0r 1-2sin²x by substituting the Phytagorean relationship sin²x +cos²x = 1)
tan 2x = (2 tan x) /(1-tan²x)
Note that double angle formulas involve a “2” somewhere, either as a coefficient or as an exponent.
These formulas are useful in simplifying and proving formulas in calculus.
11/28–Handout: 26, 32 (c), 38, let’s finish 73. HW quiz tomorrow?
11/27–Handout: 11, 17, 23, 24, 27, 31, 34, 40*, 45, 49, 57, 68*, 70*, 71*, 73* (write formulas down; after a while the formulas will become part of your DNA).
11/26–pg. 2²5²–3-6; 11-14; 47, 48
11/13–Be ready for hwk quiz on unit circle values and inverse functions. We will over the hwk assignment given on 11/12.
11/12–pg. 326–17-25 , odd ( #21 involves quadratic formula; 25, factoring by grouping–good probs to review algebraic techniques).
11./9–pg. 326: 1-12, all Strategies to use: factor whenever possible (most of the problems lead to a quadratic equation), reduce the number of functions whenever possible by using a trig identity (#8). Divide at your own risk, done rarely and carefully–more on this Monday…yes it is OK to divide, but with a very strong caveat (Geoffrey?), only when division is your last option..don’t be tempted by the looks of a problem. Ask yourself if prob can be manipulated algebraically so that it leads to a factorable expression.
11/7–Major assignment tomorrow–graphing, equations, simplifying trig expressions by using identities and algebra.
11/5–We will finish #55 from handout; Homework–photocopied pg. 322: 29-36, all (some of these probs may be laborious, don’t give up–do the obvious (again, see handout, pg. 810). Our major assignment is scheduled for Thursday, giving you an extra day of in-class practice).
11/2–Handout: 9-18, all; 19-55, odd. Some of the techniques suggested in 9-18 as well as the “steps in proving identities” (hand out, pg. 810 given out this morning) are used in probs. 19-55. On Monday we will go over the hwk (may check it); we will have a major assignment on Wed (election day Tuesday), be prepared for a hwk quiz on Monday. Don’t forget : Fall back Sunday.
10/31–photocopied pg. 321, old book (Simplifying trig expressions)2-24, even (expect a homework quiz tomorrow; hwk assignment not included).
10/30–Don’t want to spook you with a quiz tomorrow; we’ll do that on Friday…Homework: pg. 411 (text), 30-38 (follow instructions).
1o/29–See 10/24 below regarding 5.1–d0 (or attempt) 9-16, 27-29 pg 410
10/26–photocopied problems (see below about “Inclination of a line”) 25-36 (do what you can with 31-36 (we did 32 in class)..the main reason to give you this problem is to review some algebra concepts you may have forgotten as well to reinforce trig and the unit circle…have a nice weekend.
10/25–Inclination of a line–recall that the “inclination of a line” is the angle measured from the positive x-axis to the line “inclination” relates to “slope”, so as discussed this mornig, the “angle of inclination” is α = tan ¯¹ (y/x) , where “y/x” denotes slope of the line (“rise/run” or “opposite/adjacent” in terms of right triangle). Hwk: pg. 299 (old book, photocopied): 12, 13 (“class exercises”); 19-24
3/19-The main idea of today’s lesson: Be able to identify the integrand as either an inverse sine (square root, a² -u(x)² or a² -u(x)² (no square roots) which leads to inverse tangent; your numerator should have “dx” by itself. Beware that sometimes we may need to manipulate the denominator to get it into a familiar form (complete the square, for instance). HWK: pg. 393: 1, 3,6, 10, 11, 14, 17, 20,21,23,24,26,31, 32, 35, 51, 52,54
3/18–p. 378: 67,, 68 89,90 (print as required, slope fields are always compliments of Allie C, Why?) ,97-100
3/15–pg. 378: 55-58, 61, 62
3/14–pg.377 33-54, multiples of 3
3/13–pg. 386; 41, 42, 45, 46, 47, 48, 64
3/11– pg. 338: (Before finding the derivative of the inverse, determine if f(x) has an inverse. How? find f ‘ (x) and see it is monotonic, that is does f ‘ (x) change sign in its domain, is is always negative or positive? If monotonic, then f(x) has an inverse (think y = x³) )
25, 28, 50, 61,, 73-76, 77, 78, 81
2/27–pg. 357: 42-56; 62-68, even + pg. 358 (69, 70–slope fields print from www.mathgraphs.com (my printer will not be available tomorrow).
2/25–See below, 2/22 as well as pg. 348: 70, 76,79, 118
2/22– pg. 330 : 43-50, 56, 68, 77
2/21–“Free Response” Friday has a certain alliteration to it that is inviting, don’t you think? A “stand alone” FR usually counts as a “minor assignment” given the comprehensiveness (more than one topic tested) and the fact that we are timed. Thank you, Carter, for taking the initiative and assertiveness in requesting a motion problem..Class, take note: if there are any particular FR may want to see, ask –this is for the social good. HWK: pg. 330: 29-38, 41, 42 (those pesky slope fields, again!). go to www.mathgraphs.com, select your book and scroll to Ch 5 and print the pages. If you don’t have access to a printer, stop by my room during C1 or C2. A demain!
2/20– pg. 322: 72, 80, 81; pg. 330–2-24, even
2/19–pg. 322: 45-59; 64, 66, 68, 70*
2/18–pg. 321: 20-40 even
2/15–We need to work on FR, for sure. pg. 350 –111-114; 115, 117 (more slope fields, something new to annoy you or enrich your calculus experience–the choice is yours(.
2/14–Happy Valentine’s! I decided to use a ten-point scale on the recent major assignment (what was I thinking? I am not an NFL referee to overlook the obvious). Will do the same tomorrow, although I will no add points Why? 17 MC questions (one bonus included–those of you reading ahead will benefit, must show work) and two FR (compliments of Suraj) graded on the FR scale. No calculators; you will have the whole period. FRs include material from last semester (all FR do; it is not easy to find a FR that covers exclusively what we are doing now–reviewing previous stuff will keep us on our toes, so says the AP wiseman).
2/8–Major assignment on Monday.. modified AP format: 20 MC + 2 FR..please make sure you bring your calculator is set to radians–remember, decimal answers must be written to at least three places behind decimal; less than three places, you will lose a point per AP guidelines.
2/7–Please review formula for value of a function as well as the mean value theorem for integrals. Overall improvement as compared to the last quiz–remember, these assignments are diagnostic, in preparation for the major assignments next week. HW: Read 5.4 (do pg. 349: 87-109 odd)
2/6–pg. 309–65,67,62,73,76,81 (set up trapezoid rule-we haven’t been doing too many probs dealing with trap rule); pg. 311–10, 11 (compliments of Carter)
2/5–pg. 298–55-64 (63 deja vu)
2/1–Check guidelines on pg. 292..do 28, 30, 32, 42-54 (even), 56, 58, 62, 64
1/31–Ready for u-sub? Do 1-6, try 35, 39, 40–will continue with topic tomorrow.
1/30–I expect you to ask questions about the hwk given on 1/29; no questions –> you have mastered FTC..we’ll find out. Read u-sub pp 288-290–this is a topic that requires that one be observant, requiring algebraic manipulation and certain subtleties, so we’ll take it easy (examples 1, 2, and 30
1/29–pg. 286: 87 (done by Noor, but it was incorrect since she gave us a numerical answer which is not possible, pour quoi?) Now that we have discussed FTC in its entirety (those of you that came for tutorial seem to have a better understanding–Olivia and Carter are still in LALA land (I am not referring to the movie) causing confusion and obfuscation amongst the rest of us) do pg. 286, 87-96 (this is as close to AP type of questions as your book gets). Don’t rule out an assessment of some sort, si ne pas demain, peut etre jeudi, bien sur vendredi. AP question season is on (last longer than king cake season).
1/28–pg. 286: 75, 79, 81-83, 87. Review Reimann (RR, LR, MR,–right, left, and middle) as well as trapezoid..we will do a review problem tomorrow so that we can have a quiz on Wed (minor assignment).
1/25–46, 48 (we know the average (y) value; now can we find the corresponding x-value? Since the functions are integrable, anti-derivatives are differentiable and therefore continuous, so IVT applies)
1/24–The honeymoon is over…it is obvious that you have not been doing your homework, not paying attention in class, not asking the right questions or not coming for tutoring. Some of you have difficulty discerning the value of the integral and the integral as area…this is fundamental. Some of you did very well on the assignment; others, not as well. YOU CANNOT AFFORD TO FALL BEHIND; BE PROACTIVE. Now, let’s recap what we did this morning; trapezoid rule (problems in your book are not very good, so we’ll look at Stewart tomorrow). We also learned about Average value of a function which essentially adds all the values of a function over an interval (this is the antiderivative evaluated from a lower limit to an upper limit, FTC part I-this gives us the VALUE) divided by the length of the interval. Please DO NOT CONFUSE with Average Rate of Change (AROC) which is a rate of change, namely the slope. When performing integration, you are given a derivative and must find an antiderivative, i.e., a function, which is evaluated (value) from x=a (lower limit) to x= b, upper limit. Now, for homework:
pg. 284: 15, 24, 26, 44, 50, 51, 52, 61 (Dr. Bouchon)
1/22- pg. 273: 42, 45, 46
1/17–Handout on Riemann sums
1/16–have you been doing your homework? Zyad, Gui, Eddie, the usual suspects. Do pg.263–63,
1/15–pg. 263–41,48,49, 57 (wrt y-axis)
1/14–pg. 261: 15, 19, 21, , 31 (use formulas, pg. 254) Olivia is on a roll.
1/11–No assessment on Monday; HW: pg. 25o 59, 62, 64, 69, 70, 73. Read 4.2
1/10–pg. 249–23-41 (odd), 38,42
01/09–L’Hopital’s worksheet (all). Remember to use L’Hopital’s correctly, i.e., the “indeterminate” requirement is met and that we are taking the limits of the derivatives (ascertain that f(x) and g(x) are differentiable, hence continuous as x–>0). Clear?
12/13–Maybe a hwk quiz tomorrow (one FR problem). HWK: Read about L’Hopital (text, pg. 530. Why such a jump? L’Hopital’s (as it is known in cal circles) was a BC topic until 2016 and not covered in Cal AB, where it really belongs..after much consideration College Board at the behest of Cal teachers decided to move the topic to its rightful place, hence the placement among BC topics in cal books prior to 2016). L’Hopital is cool, but not to be used haphazardly (not that we ever do things haphazardly in this class)..we must meet the conditions before we invoke L’Hopital! What are those conditions? a) that the limit is indeterminate (0/0 or
∞/∞); we must also state that the f(x) and g(x) are differentiable, then we are set to go…Beware that sometimes we may have to apply L’Hopital more than once.
HWK: pg. 537: 1-20
12/12–Read http://tutorial.math.lamar.edu/Classes/CalcI/LHospitalsRule.aspx Will go over hwk probls given on 12/11.
12/11–pg. 236; 28, 29, 65, 67
12/10–Read http://tutorial.math.lamar.edu/Classes/CalcI/LinearApproximations.aspx–This is what I tried to do this morning in C3 before you got terribly confused; after the confusion in C3, I did not even attempt the topic with C4 (always use C3 as a trial). I think Paul’s notes (as usual) does an excellent job, better than your text. This is not a difficult topic–we know how to get the equation of the tangent line at a given point, (x,y)..so, we get the equation and then we use that equation to approximate the function at a given x value. This is called a “linear approximation” or “tangent line approximation”. As you move away from the point of tangency, the approximation becomes less reliable. Now, depending on the concavity of the given function, your tangent line may either overestimate (concave down, tangent line is above the graph) or underestimate (tangent line is below the graph or overestimate). Tangent line approximations are used in engineering, physics and statistics in making predictions and checking for accuracy. So tomorrow, we’ll finish two optimization problems and look at some optimization problems.
12/7– I would have finished and posted your test results, but Diensn, Fang, and Ms. Gamble stopped by to visit..so I had to catch up with current events..never a dull moment with Ms. Gamble as we know, regardless of subject matter..will work on finishing Monday during 2nd pd…so, Muntha et al (Noor, Carter, Tia, Claire, Kim, Jessica…the usual suspects), save yourself sometime, don’t check the portal..enjoy your weekend. On the agenda for Monday: go over the test (Anwar, you need to make up ASAP) and address hwk probs listed below + more optimization. Next major assignment (group assignment?) Wed 12/12 (easy date to remember).
12/6–Test tomorrow: 3o MC + 1 FR–no calculators. Focus on derivatives and their graphs, concavity, inc/dec, max/min, POI (some probs involve algebra), velocity, acceleration, etc.
12/5–5, 27, 33 Remind me to do the “Stand and Deliver” problem
12/3–pg. 6³–(Got that, Muntha?) pg. 2, 5, 9, 16, 18, 20 (b, c, d). 24 (good problem). Follow guidelines.
11/30–Read pp. 311-313, pay attention to examples 1, 2, and 3.
11/29–Handout, (Stewart, pg. 248) 20-23.
11/28–Test tomorrow consists of MC questions, FR, and a graph of the f ‘ (x) to be analyzed similar to #27 and #28 (a-d) –you will not have to graph f(x), but you will have to justify your answers. Please note: tutorial tomorrow, so please be on time..no calculators (concepts and easy to do algebra..nothing too complicated. Review IVT, MVT, and EVT, particularly the conditions (hypotheses, the “if” part, the “given”). Like Ahmed said (can’t believe I’m quoting him), “We have to move on.” (No child left behind, Muntha). The only way we have to find out where we are is by assessing 0ur knowledge.
11/27 Any questions for me? Muntha, my sources tell me that you are rather distressed about the topics we are discussing (Celia commented on the general confusion she observed in C3)..can we clear this tomorrow? 191; 79-84; pg. 201: 87, 88 + any lingering questions from previous hwk (11/26, 14)
11/26–27,37,39,61; pg. 208, #23
11/14–pg. 189; 3-6; 18-20, 24, 26 (Test for concavity–Use f ” (x) = 0 or f ” (x) is undefined, this will give you PPOI (“possible points of inflectcion”) , to identify POI, test to see if there are sign changes at the PPOI, indicating a change in concavity. Test intervals: If f ” > 0, f(x) is concave up in that interval ; if f”< 0 , then f(x) is concave down in the given interval.
11/13–Follow examples in book. HWK: pg. 181: 4,9,10,19, 27, 29, 32, 34, 43-44 (visit www.mathgraphs.com , check 7ed, go to Chapter 3, section 3.3, click on 43-48 to reproduce graphs. If you don’t have access to a computer, simply duplicate your graphs on paper as best as you can and draw the derivatives.); 62. Read about concavity. Be ready for a hwk quiz tomorrow on extrema.
11/12–19, 50-Read 3.3
11/9–As someone said, we have done enough of these critical point stuff, so let’s move on and expand on the idea. Your hwk for Monday is to read 6.2, Rolle’s Theorem and the Mean Value Theorem (aka MVT), follow examples and be able to discuss in class.
11/7–pg. 165: 13, 19, 25, 26, 27, 33 (Carter’s question)..follow guidelines on pg. 163. Note: ABSOLUTE EXTREMA can only occur in a closed interval; RELATIVE EXTREMA CAN OCCUR ON EITHER A CLOSE OR AN OPEN INTERVAL.
To find extrema on a closed interval:
- * Critical numbers occur whenever f ‘ (x) = zero 0r f’ ‘ (x) is undefined. (remember the critical numbers must be in the domain of the closed interval (Ziyad))
2. Substitute the x values found in #1 into the given function, then compare the f(x) values and determine abs max/abs min.
**critical no. refers to an “x” value; critical point, (x,y); Value, means y-ccordinate.
11/2–Read 3.1; pay attention to EVT (EXTREME VALUE THEOREM, one the “BIG FOUR”; you already encountered IVT), critical number, extrema, absolute min/max; relative min/max. Ddo 1-6, pg. 165
11/1–Hope you are enjoying your break–be ready tomorrow for a comprehensive, not necessarily difficult, major assignment. What’s in it? Well, the test is deja vu..we have done every question, either in class or assigned for homework. Limits (4–Olivia’s request); 4 related rates (one has a cast of 13, with Dr. Bouchon making a cameo appearance (she knows, and is delighted that she is honored in a math problem) some people are trolled; others, merely mentioned. Some probs use derivatives rules…nothing too hard, a bonus problem included compliments of Angel. Calculators allowed, although I would prefer exact answers (leave in terms of Π.)
10/30–Some of you may be spooked and/or surprised by the grades in the minor assignment, I was (Cecilia? Muntha?). Tomorrow we will go over the problems, pointing out what went right and what went wrong. Trick or treat? Test on Friday.
10/29–My calculus compadres sent me so many related rate probs that I had a difficult time selecting, so I selected 8 and left some good ones for the test on Friday. Groups of two(minor) assignment tomorrow (may morph into a major assignment).
10/26–pg. 151; 35, 36 (the shadow problems, after all, it is Halloween time) 39, 44–I know we have 10/25 and some probs to go over from 10/23 as well..so on Monday is HWK day…I also have some previously released FR questions I would like to discuss with you in class (or maybe give as a group assignment?) Remember, homework assignment problems are suggested problems; you don’t necessarily need to do all of them–you can be selective (I am). I know you have a life (I think), work after school, families, “friends” (do you?), interests and hobbies..use your time wisely–learn how to prioritize. I am still learning about time management.
10/25–Hwk for Friday: pg 1²7²–31 (previously assigned); 33, 40 (compliments of Dr. Bouchon), 43 (a balloon left over from Kevin’s birthday).
10/24 (Kevin K Kim’s (et al) ‘s birthday..still waiting for my cake..was not invited to the celebration :>( (this oversight will be taken into account when grading papers and writing letters of recommendation). Test tomorrow (see 10/19 + a little surprise)..no calculators!
10/23–pg. 149: 13, 14, 31 (Nick’s correction).
10/22- Hwk: pg. 149: 18-20; pg. 348: 39-46
10/19– Major Assignment Monday! Your test is a work in progress; will finish putting it together Mon morning…what to study? Derivative rules, chain rule, implicit differentiation (redundant, isn’t it? ID includes CR!), definition of the derivative, you will see a couple of homework and classwork probs that we have done (revisited), and yes, Olivia, there are limits (like there are limits to your grade). Mainly multiple choice, but I’m trying to get constructive response, which, hopefully, will not prove to be destructive response ;>) Bonus prob?
10/18 Kha Le’s problems are a good practice/review for the minor assignment tomorrow; I strongly recommend you do it.
10/17–pg. 142: 40, 41, 43, 48. Tia Williams knows how to handle setbacks, positive attitude…fails math and still smiles :) (quoted from her recommendation letter).
10/15–I hope Carter is a better driver than he is a deriver (as evidenced on his last assignment). HWK: pg. 142: 1 thru 7, 10 (compliments of Ms. Helgeson, why?, 12- 16, 24, 27, 28
10/12–Let me be explicit about this: you need to know implicit differentiation…so please read 2.5
10/05–Major Assignment 10/09–(Mainly Ch 2, up to and including Chain Rule)
10/03–9 pg. 136: 90, 92, 100, 101, 102, 104–Last day for Chain Rule. Expect an assessment tomorrow.
10/02–So, I’m here in my room after school grading the homework quiz from this morning when Patrick L and Megan K stop by to talk about college and schmooze (they were supposedly helping Olivia with HSAC planning)…which explains the delay in posting the homework and finalizing your minor assignment for tomorrow. . HW: pg. 134: 77, 80, 81 (second derivatives can get unwieldy, particularly with rational functions (think quotient rule applied twice–&^%#)). Minor assignment on for tomorrow..
10/01–Good afternoon–sorry I’m late–working on implicit differentiation problems at the request of Celia and preparing for the next topic which makes the Chain Rule seem easy (in fact, without CR there is no much we can do and without Implicit Differentiation, what is there to differential calculus).. We are getting better with the CR, but I feel we need more practice, right Noor? So: pg. 133: 47, 53, 56, 58, 61, 64–we will have some fun with probs from Stewart as well…ah, yes, probably a hwk assignment at the suggestion of Kevin Kim. (CR not included).
9/28–Calculus is torture now we are being chained, like in the Chain Rule (I know this is lame)–Minor assignment (20 minutes)–review basic differentiation rules (relax, Muntha’, CR not included). HWK: (good practice for the minor assignment) pg. 133–21, 24, 30, 33, 38, 43, 47
9/27– As per Ms. Russo’s suggestion, no homework tonight due to Open House.
9/26–Be ready for a homework quiz tomorrow. Homework: pg. 115; 91-98
9/24–It is 7:00 PM –How many times have you checked the wiki, Muntha? At least three? Just sayin’…OK…got inspired and decided to change the test a bit…so, here is what is in store: About ten multiple choice questions, a drawing (Ahmed asked..given certain conditions, similar to one we had before0, ∼ 85% limits, open ended questions that you have to explain, probs that you have to work and arrive at a conclusion..Suraj and Neel think it is a good test…yes, derivatives are included. No calculators!
9/21–On Monday we will go over all the hwk assignments pending. Also: hwk on product and quotient rules, pg. 119:–11, 30, 34, 52, 54, 57, 60, 67, 75. Probably have a hwk quiz on Monday. Major assignment on Tuesday.
9/19–pg. 116–101, 102, 107, 111–Eddie and Shivan you can dance (yes, we want an encore-the BEST number in the pep rally, worth my attendance! synchronized and symmetric)..now, can you do calculus?
9/18–pg. 114: 55,61, 66, 76,89,91
9/14–Test Major Assignment Qu’est que nous avons avoir? Make use of graphing calculator to make inferences about a graph (calculator should be in radian mode in this class always (Kevin Kim), limits, continuity, T/F, definition of the derivative, IVT…Email me if you have any questions about the hwk assignments (9/13 and 9/11-.. Read about sum, product and quotient rules.
9/13–pg. 103: I will do 47 and 48 in class; your hwk: pg. 113: 14, 18, 64, 62
9/12-As people in Carolina prepare for Florence, you should prepare for either a hwk participation grade or a minor assignment tomorrow on any topics we have covered so far (yes, Olivia, that includes limits…how can we forget about limits?). I haven’t decided yet on the format…let me look at the archives and suggestions from my cal posse.
9/11- pg. 102-47-49; 66, 70-80; 85, 86
9/10–pg.102: 8, 22, 30, 34, 36
9/6–Read 2.1..tests have been graded and posted!
8/31–Please be on time for your Unit I Test on Limits. What’s on the test? Everything! (only one prob requires trig functions). Every prob has been discussed in class and/or assigned for hwk (some are deja vu). Some you can do by inspection. A couple of probs are AP style in wording or origin. After our class Friday and your two minor assignments, I think you are prepared. Trick probs? maybe 2, but this is a matter of perception…I prefer to say ,”probs that make you think”. No calculators (no need to reduce answers); you must work diligently and write clearly and beautifully! . You will need scratch paper!
Have a nice weekend! Don’t spend too much time studying (Muntha, Noor et al); Happy 16th, Channel (test is my belated bday present to you; now, present me with a good grade). Tia, I think you will find the test doable and tolerable. Celia and Carter, now is my turn to ask you questions. ; > )
8/30–pg. 199: 19-24, 29-32. Remmeber: use dominance if possible or manipulate expression if possible.
8/29–Read 3.5 (again!), paying attention to example 4. You should be able to do 1-14 in your study guide.
8/28–ma tomorrow; MA Friday–Tomorrow continuity and (graphically and analytically), IVT, limits…
8/27–Read 3.5 in your text book ( pp. 192-198) and complete handout given tonight (hwk); use your calculator as needed; we will discuss how to find horizontal limits analytically tomorrow. Start reviewing for major assignment on Friday (more info later).
8/24–Handout on composite functions; minor assignment Tuesday 8/28 (limits and continuity).
8/23–Tomorrow is hwk day..that means we will go over all hwk probs from 8/21-today) add pg. 77: 68, 75, 83, 86
8/22..Add the following to your hwk–57-60 , 69-72; Read about IVT (necessary condition: function must be continuous on an interval).
8/21-Later than I expected (Carter and Celia, pls remind me to do probs 83-84, pg. 66..overdue). Now, for continuity: pg. 76: 13, 14, 25-32; 34-48 (even)
8/17–Homework Quiz on Monday (remember these count for 20% of your grades)..All the probs have been either assigned for hwk or discussed in class, short quiz, I expect most, if not all to well; I think you are ready, don’t disappoint me. I hope to return your graded quizzes Tues so that we may have a minor assignment (a bit longer, 30%) on Wed 8/22 —I will not give you a minor assignment unless I have finished grading the quizzes! Those of you who have had me before know that I like to return assessments ASAP. We will tied up a few loose ends on Mon before the quiz (such as the hwk assignment given on 8/15, how to graph piece wise functions in the calculator (C4, the last prob we did was input incorrectly, which is we were getting only one graph which appeared to be continuous at x= 0; we’ll correct this on Monday (remind me Celia, Olivia or if your name ends in “ia” Tia?)
8/16–Quiz postponed–Monday, 08/20 (sorry to disappoint you,Noor et al, but I’d like to look at a few more problems from other books, and start on “continuity” and piece wise functions).. Suggested by Carter: (use your calculator so that you may have a better understanding): pg. 66: 89-84 (In physics and engineering the algebraic function that multiplies a trig function( either the sine or the cosine, why?) is called the “damping factor” and acts as the “amplitude” (remember graphing y=a sin (x) where “a” is constant? Well, you were doing a variation of the “squeeze”/”sandwich”/or “pinching” theorem (depending on the book you are using–“Squeeze” is by far the most common and logical)–I think I will name it the “Carter Nugent” theorem, at least for now or the “Adrija” Theorem). PLEASE READ 1.4, paying attention to boldface terms and main (boxed off in rectangles).
8/15–pg. 67–101-104 (compliments of Dr. Bouchon ; don’t spend too much time on these problems, however), #122; “Getting at the concept” (95-98).
Tomorrow we will finish going over probs 83-86, pending from 8/14, address the hwk for today and look at how other authors approach ” limits” and work probs from other sources. Quiz on Friday! Don’t despair…yet!
8/14–pg. 66: 67-86
8/13– pg. 66: 56 -62 (care to comment anyone? For those of you who have been reading ahead (or at least have led me to believe that you are reading ahead), do these probs look familiar? )
8/10–Read pp. 50-51; do pg. 55: 9-18 (graphic interpretation); pg. 65: 27-34 ( time to review the trig values of special angles..unit circle, ASTC), 41-44; 49-52