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# PRECALCULUS

10/19–Assigned probs form *Trigonmetry*, (Hornsby et al; pg. 273; 7-16)

10/18–photocopied pg. 306 (19-24). I suggest graphing these probs first (radian mode, Zoom 7, 0 ≤ x < 2π) to find the solutions graphically). Remember that the main concern with these problems is the period.

10/17- Finish problems on handout (5-7)

10/16–Handout, 1-4 (use graphing calculator as needed)

10/13–I’ll be checking the hwk assignment given on 10/9 (see below) for a participation grade. If you haven’t done it, please do it.

10/10–Good luck on your PSAT demain! On Thursday we will have a retest (make up) in class. Your test grade from 10/9 will not be dropped, however.

10/09–Grading your papers, I was hoping that this test would elevate your grades but you seem to be having problems with angle of elevation (Nick, Chris) and angle of depression (which describes my present state). HW: pg. 358 (3+5=8, love # combinations: 58, 60, 61, 68, 72-76 (my blood pressure is going ↑).

10/6–See 10/5. We worked fined tuned our graphing tools this AM and you should be ready for the test next time we meet, hopefully Monday..we are at the mercy of Nate..remember: if you play now, you pay later..so if we have days off, we will have to make them up…disruptive. Reginelli’s is closed this weekend (2 PM Sat), so, time to study. Maybe this hurricane will blow some trig your way and make it stay.

10/5–Possible hurricane tomorrow..uhm, I mean “test”..including applications of right triangles and a bit of graphing similar to what we have done in the past two days + some all stuff (it is always good to review what we have learned). No hwk per se as we have not finished going over all the graphing. Recommend you bring a scientific calculator.

10/4–Old book, pg. 313, whole page; pg. 395 #25

10/2–Same as 9/28

9/28–Photocopied page, old book (pg. 305; 1-16). Additionally, pg. 336: 61, 62, 394: 8,15,16,22

9/27–pg. 357 (three consecutive odd #s)–29-40; 43-48..Read 4.4 and come ready for questions. David asked,”What happens if “B” is negative”? In your graphing utility graph y = sin (x); y= sin (-x) AND y= cos (x); y= cos (-x) . What do you notice? Why? Why does your book mention abs (B), but other books don’t? Ponder on that. Test on Friday, 9/29.

9/25–See 9/22

9/22–Test (Major Assignment on Monday, 9/25). HWK: Study Guide (photocopied pg. 293, old text..good review guide)

9/21– HW: old book, photocopied pg. 289; 5-8 (bottom); pg. 290: 11-12. We will go over the hwk before the minor assignment tomorrow.

9/20–pg. 385: 1-12 (all); 23-32, 33-35 (expect a hwk quiz tomorrow)

9/19–pg. 385; 1-12, except 4, 5, 8, 11

9/18–Read 4.7–Inverse trig functions..we will be on this topic for the remainder of the week. Bring calculator. When doing an inverse trig function problem, the answer is an angle in a restricted domain. Why? Because the trig functions fail the horizontal line test due to periodicity, we must restrict the domain as we did in our discussion this morning ( y = x² has an inverse for x ≥ 0) in order to make them one-to-one (a “one-to-one” function is a function that passes the vertical and horizontal line tests, i.e, both the fn and its inverse are functions).

9/15–We covered the graphs of the six trig functions. Review the graphs carefully. You should know the domain, range, period, continuity, whether the functions are bounded or not (only sine and cosine are), increase/decrease intervals, even/odd, asymptotes–there is a nice summary at the bottom of pg. 364 (I also gave you a hand out this morning which did not include y= cot (x)).

The minor assignment scheduled for Friday will be given on Mon, 9/18. HWK: Do cot x on the last pg of the handout and pg. 365 (how many days in a year?), top, 5-10.

9/14–Minor assignment tomorrow: review reference angles, unit circle, values of special angles. We will go over the hwk assigned 9/13 before the quiz.

9/13–Judging by your hwk quiz today, you need to study the trig values of special angles ☹️. HWK for tomorrow: pg. 286: 13-18, photocopied.

9/12–Expect a hwk quiz tomorrow on trig values of special angles (we’ll be on this diet for a while). HWK: assigned problems from photographed (not twitted) hwk, (sorry, Hyobin, twitter queen).

9/11–Today we derived the trigonometric function values of special angles (30, 45, and 60º or π/6, π/4, π/3) and their multiples by using right triangle and cofunction relationships. It is important that you familiarize yourselves with these values as we will encounter special angles often in this course, calculus and physics. HW: old book (please try not to use a calculator, although you may consult the table..I don’t memorize, but draw a right triangle as needed. For a 30-60-90, always associate the shorter leg with 1/2). Remember: in Q1, all values are +; in Q2, Q3, and Q4, two trig values are >0 and the other 4 trig values are <0. Where is x>0? where is x<0? y>0; y<0 (ASTC kicks in as a mnemonic device). Associate y with sin Θ; x, cos Θ

HWK: phtocopied pg 280, 11-18.

9/8–pg. 347: 37-42

9/6-pg. 348: 43-48 (use reciprocal relationships–see handout). Please bring hand out tomorrow.

9/5–pg. 347 (3+4=7..we keep getting all these arithmetic relationships), 1-20, all

9/1–Don’t forget: Reginelli’s will donate 10% of your food bill Sat evening (9/2) towards Hurricane Harvey release efforts. As an extra bonus, you’ll get to see Bennett and Hyobin (Clearview location) and have a Dream State or Uptowner on foccacia on my behalf (my favorite). Also, on my behalf: HW ( photocopied pg. 279 (2+7 = 9)): Written exercises (A, bottom of page), 1-4 all. We will have a minor assignment on Wed 9/6; enjoy your long weekend.

8/31–Phtocopied pg. 274; 33-40

8/30–Phtocopied pg. 272(old book): 1-19, odd; do 5 and 6 as well

8/29–pg. 273: 21-29

8/28–Read 4.2..relate right triangle trigonometry to the unit circle.

Look for trig values of special angles.

8/24–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).

8/23-photocopied pg. 262: 17-23, odd

8/21– 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 .) , pg. 325–25-33 (odd); 35-38

8/18–1-24 (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”).

8/17–pg. 95: 25-28; 35-40

8/2(8)–pg. 95: 9-16 (state domain and identify the function); 47-54 (remember the tests: If f(x)= f(-x), even, symm wrt y-axis; if f(-x)= -f(x), odd, symm wrt origin)

8/15–pg. 116; QR–1-10 (for help refer to sections indicated). Re-read 4.1. We will probably have a quiz on domain on Th.

8/14– We will continue our review of functions learned in Algebra II. Meanwhile, read 4.1, pay attention to new terms: radian measure and conversion from degrees to radians (we will explain further tomorrow). This is a reading homework assignment. Also; do pg. 94: “Quick Review” (QR) : 5-8 (find the domain–good quiz questions)

**CALCULUS AB:**

10/29–HWK: Read 7.7, When do we use L’ Hôpital? When direct substitution produces an indeterminate form (the form most commonly tested on the AP exam is “0/0”). Pay attention to the theorems on pg. 531, particularly 7.4 (explained by our friend Neel and our “friend” Zunair). L’ Hôpital was originally (years ago) a topic covered in Cal AB, then it was moved to BC, a move that always mystified me; as of last year, the topic was kicked back to AB, which is where it belongs (tested on last year’s exam). I prefer to work a limit problem by using direct substitution or one of the methods learned in Ch. 1. However, I find L’ Hôpital convenient. In order to invoke (use) L’ Hôpital, you must ascertain that direct substitution gives you an indeterminate form and then state ,”by L’ Hôpital….” . Now, for hwk (i know, Zunair, less is more, but I am taking lessons from Manal), pg. 537: 5-20 (omit 18, unless you know the d (ln x)/dx (Hassan M knows).

10/18–How do we find the derivative of an absolute value function at the points where it is differentiable? Refer to prob 104, pg. 136 (proven in class this AM), Now do pg. 136, 105-108. Tomorrow, L’ Hôpital rule (Neel and Suraj, are you ready?)

10/17–Major assignment tomorrow: implicit differentiation, tangent and normal lines, limits, potpourri..

10/16–Handout–Since you did so well on the participation assignment this morning, perhaps you would like another for tomorrow? I’m in.

10/13-Minor assignment on “Implicit Differentiation” Monday, 10/17.

10/10 HWK–pg. 142: 24, 26, 28, 35, 43, 48 due 10/12. Good luck to the juniors on their PSAT. See you on 10/12 (with the test graded); Minor assignment on Friday. Chain rule? Trig derivatives? Unit Circle?

10/9–Je ne vais pas ajouter plus des questions a votre examen pour demain, meme si Justin Hugger veut que j’ajoutte la regle de chaine. Test is wort 31 points (will have a bonus point on the board) and I will be adding extra points if you have any (we know Nicole and Zunair have at least one each for being absent). HWK for Thursday, 10/12 (no class 10/11..I will miss you..NOT!). pg. 142: 24, 26, 28, 35, 43, 48. Hope to have the tests graded by Th.

10/6–Test on Tuesday. whether we have school on Monday or not. . HW for Monday (Yes, I think (hope) we’ll be in school Monday pg. 142: 1-15. odd). Now, if we don’t have school on Mon and Tue, then we’ll have the test on Thursday, but I don’t think this option will materialize. What do yo do on a rainy weekend? Math hwk and catch up with your resume (Nameera), brag sheets, college essays..I’ll be writing LOR and catching up with other cal teachers, my BFFs..maybe this hurricane will blow some calculus your way (study limits, continuity, IVT, tangent lines, normal lines, etc…test could have been given to you two weeks ago..no chain rule or derivatives rules on this one).

10/5–Will return test from Tue 10/13 tomorrow..maybe a participation or minor assignment? Read section on “Implicit Differentiation” and pay attention to the examples..ask yourself, “what’s this stuff”, “when and why do we use it”?

10/4–Handout from Stewart book (Zunair is checking SLADER for answers since he is apprehensive about my collecting homework): 29, 32, 34 ,43, 45, 51, 53-57

10/3–Test tomorrow, Ch. 2 , up to but not including Chain Rule (we’ll get that later, Justin..no estan listos todavia).

10/2–Bruno may be a careful driver, but he is a distracted deriver! Chain Rule ..we’ll be on this topic for two days (at least); the problems in the book can be labor intense due to the algebra (we call this “cleaning up the problem”) and may not be representative of what you may see in the AP exam. So Hassan, how far do we need to go? OK, if you can factor and simplify, do it; if not, then why bother? Common Factor, simplifying a fraction (reducing), combine like terms…be careful with negative signs (like we are careful with negative people..don’t worry about “zero” people since they don’t count). Still with me? OK, here is your homework:

pg. 133: 21, 24, 27, 30, 33 (you need practice with the quotient rule); 37, 38( chain rule is not necessary; may use power rule), 43, 47, 53, 56, 58, 61, 64…NO TEST TOMORROW! (Thank your advocate, Lisa Pham), but expect a participation grade (5-6 questions) on topics already covered (No chain rule and no limits, Allie S.)

9/28–We will go over the hwk assignment from 9/26 that were not addressed this AM before the quiz tomorrow. The quiz tomorrow will focus on quotient and product rules (2.3)

9/26–Thank you, Zunair, for reminding me about posting the hwk assignment (+1?): pg. 124–72. 76. 83-88, 93-98..Maybe a participation grade tomorrow or a minor assignment…pret la regle de la chaine? la regla de la cadena? the chain rule?

9/25–Allie A and Greer K posting hwk @ 1: 20 PM (a rarity): pg. 124; 43, 46, 48, 47 (redux, using the derivatives we learned today), 54, 59, 61, 78 (Hassan M’s question..well, one of the many),

9/22-pg. 116 #106; Practice the quotient rule: pg. 124: 11, 12, 18,26, 27, 30,31,33,37,38, 47,57–Don’t forget–practice all the rules (we will also go over the hwk assignment given on 9/21)…will Monday 9/25 be a good day to collect the hwk and give a participation grade? With something to think about, this is Mr. Hernandez signing off wishing you an enjoyable weekend.

9/21–pg. 124: 5, 6, 17, 31, 39, 40, 50, 52, 53 as well as pg. 115: 93 , 97, 98 –We will have a minor assignment tomorrow–focus on power rule, definition of derivative at a point and probs similar to hwk from 9/20 and 9/19).

9/20–pg. 115: 91, 95, 96

9/19–pg. 114: 75, 89, 90 101, 107, 111

9/18–We learned formulas for the derivatives of : a constant fn, a polynomial (power) fn., sine and cosine fns, the sum/difference of two continuous fns. Tomorrow we will learn the product and quotient rules (the derivatives of the product and quotient of two functions). Remember that for the derivatives to exist the functions have to be continuous on their domain. We also learned how to graph the derivative of a function by using the nDer command (Found under “Math 8”—NDer( y, x, x); NDer(y,x,#) gives us the numerical derivative, a value (please note “#” means number, not hashtag in this case..the “#” has been around forever, long before the current hashtag interpretation..there was a world before you discovered it). HWK: pg. 113, 3-48,(multiples of 3), 57, 62, 64, 66. Hope to return your papers tomorrow.

9/15–Read 2.2 Neel (C2) and Suraj (C3) will devlop the proof for us on Mon (proof relies on the binomial theorem).

9/14–Test tomorrow (major assignment). MM (and others, I’m sure) would like to know what’s on the test? The test is a combination of FR and MC questions; I expect you to show the work for ALL questions, including the MC. Topics? Limits, continuity, domain and range, Sandwich Theorem, limits at infinity, vertical and horizontal asymptotes, instantaneous rate of change (IROC, for future reference), review whether a function is odd or even (odd: if f(-x)= –f(x); even, f(x)=f(-x) or in plain English, “odd, if substituting “–x for x” gives the opposite (negative) of f(x); even if substituting “-x” for “x”, returns original function) y=x³ and y=sin(x) are odd fns; y=x² and y=cos(x) are even fns (in fact, all trig fns EXCEPT cos(x) and sec (x) are odd fns). BONUS PROB UPON REQUEST.

9/13–Remind me to do #32, pg. 102; also, 39-44, 46, 66, 70, 85

9/12–37,38. Gracias, Bruno, your visit enlightened me.

9/11–Using the definition of derivative lim Δx–>0 ((f(x + Δx) – f(x))/Δx) (slope of tangent line, instant rate of change) HWK: pg. 102–8, 23, 31, 34 ( Spoiler alert: messy algebra may be involved)

9/8–Test on Monday–You will need your graphing calculator for some problems (make sure you have batteries (Sophie)). What’s on the test? IVT, Average values, limits at infinity as well as infinite limits, you will have to illustrate certain situations dealing with continuity, VA, HA (no slant, Hassan, not this time). I am keeping the sandwich in the fridge.

9/5–Pls see below

9/1–On Tuesday we will finish limits at infinity, discuss dominance, slant asymptotes and look at exponential and log functions. Minor assignment on this topic on Wed (Greer feels a sense of relief). HWK: (same as 8/31 which some of you did not do due to attending the game (MM?) plus: 33, 35, 37, 38 (use hint). Remind me to investigate the special limit lim x—>∞ (1 + (1/x))^ (x) (Neel, please develop the algebraic proof).

8/31– Magnetize your brain: pg. 199: 25-32 (algunos problemas interesantes–Squeeze Theorem comes into play..don’t forget about the Squeeze Theorem for it will not forget about you).

8/29–Tests from Mon will be returned tomorrow (abbreviated classes, less time to commiserate). Today we looked at “limits at infinity) or lim x–>∞, aka, “end behavior”, which gives us a horizontal (HA) or slant asymptote (you will not see the latter very often). We specifically looked at rational functions ( Q(x) = P(x)/R(x)), where the numerator and denominator are algebraic expressions (polynomials). In general, divide both num and denom by the highest degree (exponent) in the expression, then see what happens as x–>∞. Short cuts discussed in class:

- if both num and denom have same degree, then lim x–> ∞ = ratio of leading coefficients = y
- If degree of numerator < deg of denom, then lim x –> ∞ = 0 and HA y= 0
- If deg of num > deg of denom, then lim x –> ∞ is ∞ and we may write, “DNE”. In this case we obtain a slant asymptote and perform long division to get the equation of the asymptote

The above is summarized on pg. 195 HWK: pg. 199 15, 17; 19-24 (all).32

8/28–There is nothing better than to snuggle with a calculus book and work calculus probs while it is raining outside..along those lines, read 3.5, ‘”Limits at Infinity” pp. 192-198.

8/24–Infinite limits occur at vertical asymptotes. Remember to always check your domain. Hwk: 24-28; 32, 42-48, 58,60, 62

8/23–pg. 77: 41, 45, 46, 48, 49, 52,62.63,77, 83,86

8/21–Some of you had a total eclipsed; some, partial and some none at all..HW: Review 1.4 (one-sided limit, continuity and IVT (fn must be continuous!! is a solar eclipse continuous? Yes, while it lasts, particularly in its totality path) pg. 77, 15-20, 69-72

8/18–Hope the eclipse on Monday, won’t eclipse your recent grade (we will be finding limits algebraically, much to David Hutton’s (aka “David Lampo”) delight.

HWK: Read 1.4–do 1-14, pg. 76

8/17–Same as /16

8/16–Please remind me to collect fees.. We will go over probs 67-78 (assigned yesterday, not addressed today); pg. 66: 79-82, 84; 101-104 (compliments of Mr. Prentice). Quiz demain? Peut etre…

8/15–pg. 66: 56 (use conjugate), 58, 59-62 (care to comment Suraj? Andrew? Alex? do these probs look familiar? Umm..l’ avenir nous attends). in +: 67-78

8/14–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