Welcome! Please feel free to email me octavio.hernandez@jppss.k12.la.us

# PRECALCULUS

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

12/4–Read 5.5

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

11/14–Minor assignment–equations.

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

10/24–Let me know if you have any lingering questions from the handout (#29?). Read 5.1 (“Identities” –pay attention to examples and highlighted material in blue rectangles (we have discussed some of this stuff already)). HW Quiz?

10/23–Handout, pg. 653 as 10/22–all probs except those assigned on 10/22: let x= prob# Your domain: All x, x≠ 3x, where x is an integer.

10/22–pg. 653: 3-33, multiples of 3.

10/19–pg. 306 (old book), 19, 20 (a-c); we will do probs similar to 21-26 in class Monday (the latter require a calculator and the application of inverse functions).

10/18–Major or minor assignment tomorrow on graphing, please bring you graphing calculator.

10/17–pg. 305 (photocopied, old book): 11-16 plus text pg. 358, 74-76. Minor assignment on graphing Friday, 10/19

10/15–As per your request, we will finish going over hwk assigned on 10/12. In addition: pg. 358: 72, 73

10/12–Handout: application of sinusoids, 1-7 (use graphing calculator; adjust window as needed).

10/11–Teacher absent; special assignment given

10/04–Chapter Test tomorrow

10/03–Handout: 52, 60, 61,75-78

10/02–Tomorrow we will look at transformations of tan, cot, csc, and sec graphs…HWK pg. 395 (8, 16,22–similar probs will be on your next major assignment Friday)

10/01–In the handout from the Sullivan book (pg. 595): 67-73

9/28–Test on Monday…there are a few questions on graphing although you won’t have to graph.

9/27– As per Ms. Russo’s suggestion, no homework tonight due to Open House tonight.

9/26–Read 352-353; do 1-6 pg. 357 (How do we obtain the graphs from the parent function, y= sin x? What is the new range? )

9/24–Check portal for graded minor assignment administered this morning..need to review a few things before our major assignment tomorrow.. Please review inverse trig functions as well as the graphs of all trig functions including domain, range, continuity, even/odd, etc.

9/21– Study guide(Chapter 7 review, old book). Minor assignment on Monday, 9/24; major assignment (similar to your study guide) Tuesday.

9/20–pg. 385: 1-12–Remember that inverse sine(x) and inverse tan(x) will yield a negative answer if x<0; positive if x >0. The inverse cos(x) yields an angle in Q2 if x<0. Remember that inverse trig functions are restricted to two quadrants and we are not dealing with the whole unit circle–there are no answers to inverse trig functions in Q3. Review the graphs, domain and range. See summary of graphs on pg. 399.

9/19–You did not have questions about the hwk assgn given yesterday which makes me suspicious as to whether you did it..You probably will see a similar problem in a major assignment next week. For tomorrow: Reread 4.7, paying attention to the inverse tangent and inverse cosine graphs (how are they restricted? Domain, range? Why is the inverse cosine restricted from 0 ≤ y ≤ π? Why is the inverse tangent restricted from -π/2 < y<π/2 (compare with the inverse sine)). For homework; pg. 395 22, 25

9/18–Read 4.7 –“Inverse Trig Functions”–pay close attention to highlighted material; we will be discussing this topic for the next two days.). Written homework:

pg. 394: 8, 15, 16

9/17–Handout: 93, 94

9/14– Handout: 79-90

9/13–Handout: 31-24, odd. Minor assignment tomorrow: You are expected to know the following: the sign of a trig function depends on the quadrant in which the terminal sign of the angle lies;. Reference angle (example: express the sine (-310 ) in terms of its reference angle. Solution: terminal side in in quadrant I (negative rotation); reference angle (-310º – (-360º) or 50º, so sin (-350º)= sin (50º). If sin 350 = – sin 50. Why? B /c 350 is in Q4, and the sine is negative in Q4, but all reference angles have positive trig values since all reference angles are in Q1. Also, trig values of special angles 45, 30, 6o and their multiples. Also, if given a trig function in a certain quadrant, find the remaining five functions. I have been discussing degrees in this blog, but you will have radians as degrees on your assessment tomorrow.

9/12-Handout: 9-30–The purpose of these exercises is to reinforce not only the trig values of special functions, but reference angles, odd/even relationships (remember only the cos and its reciprocal are even functions, i.e., symmetric with respect to the y-axis f(-x) = f(x) look at the graph; the other trig functions are odd); Pythagorean relationships (sin²θ + cos²θ = 1 which can be manipulated to yield other relationships), cofunctions (#24) and reciprocal relations (23). DO NOT USE A CALCULATOR–doing so defeats the purpose of the assignment + you will not have a calculator available for your assessments. However, I encourage you to use your handouts and notes. Review the cosine and sine graphs (domain, range, even/odd, continuity, periodicity).

9/10–pg. 349: 67-74

9/6–Read 4.4 (pp. 350-351) Basic Functions: The Sine and Cosine Functions-graph them in your calculator--make sure you are in radians! (y1= sin x; y2=cosx), Zoom 7, check your window (you may want to restrict it to one rotation to match the unit circle). Where does it cross the x-axis (angle), what are the max/min values? Compare to the unit circle.. Graph y1 and y2 simultaneously..where do they intersect? Where is the sine graph increasing? decreasing? answer same for the cosine. Where are both sine and cosine negative? positive? We have a lot to talk about.

8/31–Expect pop quizzes on the unit circle and trig functions of special angles daily. Hwk: Handout, 42-74, even (you may use any short cuts discussed in class this morning (e.g., reciprocal relationships, Pythagorean relationships (sin ²θ + cos²θ = 1, or any variation as discussed in class this morning). The idea is for you to feel comfortable using the unit circle…Remember the mantra: All answers are in the unit circle!

8/30–Hwk: Handout, 41-73 (odd nos.)–What is the purpose of this assignment? Reinforce trig values of special angles (use unit circle if needed, quadrants, reciprocal relationships..FYI: (sin θ) ² is written as sin²θ ; in your calculator is entered as sin (θ)².

/29–Complete handout given this morning (unfinished homework quiz) + pg. 348 (text) 43-48 (good probs..in what quadrant is the angle in question? )

8/28–Hwk: photocopied pg. 279, Written exercises 1-4–state whether ans is + or neg. What relationship is there between a given angle θ and any angle coterminal with θ? Tomorrow we will go over pending hwk assignments ( 8/23 and 8/24 as well as the hwk given today) before your hwk quiz. ALERT: PLEASE REVIEW UNIT CIRCLE AND TRIG VALUES OF SPECIAL ANGLES, PARTICULARLY QUAD I (INCLUDED IN NEXT MINOR ASSIGN, FRI).

8/27–Go over notes and worksheet given this morning..We will go over the hwk assignment given Fri (see below).

8/24–pg. 347 (3+4=7): 25-42 (see if you can answer without using the unit circle–reference angles (Hint: Look at the denominator if in PI radians; also consider the quadrant to determine the sign).

8/23–Review the unit circle (hand out–pay attention to special angles). Hwk: pg 383, 3-20 (even)

8/22–Read pp. 330-332 (“Two Famous Triangles” aka 45-45-90 (right isosceles triangle) and 30-60-90..these triangles form the basis of your journey in trigonometry) as well as section 4.3 (“Trigonometry Extended: The Circular Functions” (SOCAHTOA goes circular!)) Bring hand out tomorrow!.

8/21–photocopied pg. 266: 19, 20

8/20–A couple of you had questions about #13 (“rpm” means “revolutions per minute”, i.e. the number of rotations in one minute..one rotation is 36o° or 2π radians). Minor assignment scheduled for tomorrow: convert degrees to radians, area of a sector, arc length, (Key: Θ = s/r). Will go over 13-15 tomorrow before the quiz.

8/17–pg. 265–(photocopied)–11-15

8/16–Length of an arc (s= Θr, if Θ is in radians; (Θ/360)* (2πr), if Θ is in degrees). Area of a sector (a sector of a circle is the region of the circle bounded by two radii and an arc of the circle, think “slice of pizza”) If Θ is in radians: (Θ/2)* r² or (sr/2)..Which formula to use? Well, it depends on information given in the problem. Remember: anytime you are using radians, think Π. Homework: pg. 265, 3-10 (photocopied, old book). Maybe quiz tomorrow–converting from degrees to radians and vice versa; co terminal angles. Check your book, 328 #71.

8/15–pg. 335 (x3–this means “multiples of 3”); 29-30, all (follow directions).

8/14–For the hwk, use the formula Θ = s/r (definition of radian measure; formula may be manipulated as needed REMEMBER: Θ MUST BE IN RADIANS in order to use the formula .) , pg. 325–25-33 (odd); 35-38 (# 37 was discussed extensively in class this morning, thanks to Danielle P. who took the initiative to do the prob last night :) )

8/13–pg 325: 1-24 (all; you may use a calculator, although not needed (1-8). For probs 9-16, you want the degrees to cancel, so multiply by (π/180º); for 17-24, multiply by 180º/π, cancelling the π. For #23, “2” means ” 2 radians” (remember that π radians ≅ 3.14 radians–think “unit circle”). See formulas pg. 322

8/10–Read 4.1– 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).

**CALCULUS AB:**

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