Assignments

Sunday	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday
27	28	29 p. 278 # 7-18 + 35-38 8:30 AM	30	1	2 Watch “Newton’s Method” from Dr. D. Jerison (MIT) then watch an example from Dr. Breiner (Fordham University) (all links below). Then, work on p. 279 # 39,41,45 (only part "b", the Newton's Method exercise) + p. 287 # 3-15 odd 8:30 AM	3
4	5	6 Watch the video in the link (examples of De L'Hospital rule and when it fails) Then solve exercises p. 304 # 13-33 odd. For #21-31 use DeL'Hospital's rule. 8:30 AM	7	8	9 Two things to do: A) Consider the following theorems: Fermat's theorem, Rolle's theorem, and Mean Value Theorem. For each of them remove one of the hypotheses and find a counterexample that shows that, without that hypothesis the conclusion does not hold. Repeat this twice per theorem. For example: what if you remove the condition that the function must be differentiable in Rolle's theorem (but you keep continuity)? Can you show that the conclusion is not necessarily true? B) Complete the paper "Theorems with a name", that is: i) prove Fermat's theorem in the case c is a minimum ii) Show that Phi(a)=Phi(b) in Cauchy's theorem iii) Go over the proof of the first and third corollaries of MVT (consequences of the MVT) and prove what is left as exercise. 3:30 PM	10
11	12	13 Complete the Related Rates paper (attached below). Then review for Tuesday's quiz. Your quiz will (possibly) cover up to the theorems that we did (including consequences to MVT). 8:30 AM Quiz #3 9:46 AM	14	15	16 Study section 5.4 (curve sketching). Watch all video-clips in the links below about curve sketching. They might seem a lot, but they are well done and these should be enough to understand how to sketch the graph of a function using it's derivatives. Then use what you learned and graph the functions (and submit your work) from exercises p.359 #25 and 26. Of course no calculators are allowed. 8:30 AM Solve p. 366 # 1-11 odd. Follow the steps that we showed in class. This homework is due at the end of the day on Friday, so we can go over questions if you have any during class next time. 3:30 PM	17
18	19	20	21	22	23 Solve the exercises in the worksheet below. They are due Tuesday at the end of the day. Deadline moved to Friday 10/23/20 at 8.30am 8:30 AM Use the guess and check method to find the antiderivatives of exercises p. 379 # 21-35 odd Draw the slope field of the differential equations p. 557 # 3 ,5 ,7 (only the slope field). Use the points with integer coordinates from (-3,-3) to (3,3) 8:30 AM	24
25	26	27 A) Solve exercises p. 557 # 14-18 + p. 559 # 3-7 B) Study for the true/false quiz on Tuesday. Especially review important results, theorems (IVT, MVT, Rolle, etc...) and their consequences. 8:30 AM	28	29 Solve p. 449 # 9-20. Use either guess and check or the addition technique. 8:30 AM	30	31

27

28

29

p. 278 # 7-18 + 35-38 8:30 AM

30

1

2

Watch “Newton’s Method” from Dr. D. Jerison (MIT) then watch an example from Dr. Breiner (Fordham University) (all links below). Then, work on p. 279 # 39,41,45 (only part "b", the Newton's Method exercise) + p. 287 # 3-15 odd 8:30 AM

3

4

5

6

Watch the video in the link (examples of De L'Hospital rule and when it fails) Then solve exercises p. 304 # 13-33 odd. For #21-31 use DeL'Hospital's rule. 8:30 AM

7

8

9

Two things to do: A) Consider the following theorems: Fermat's theorem, Rolle's theorem, and Mean Value Theorem. For each of them remove one of the hypotheses and find a counterexample that shows that, without that hypothesis the conclusion does not hold. Repeat this twice per theorem. For example: what if you remove the condition that the function must be differentiable in Rolle's theorem (but you keep continuity)? Can you show that the conclusion is not necessarily true? B) Complete the paper "Theorems with a name", that is: i) prove Fermat's theorem in the case c is a minimum ii) Show that Phi(a)=Phi(b) in Cauchy's theorem iii) Go over the proof of the first and third corollaries of MVT (consequences of the MVT) and prove what is left as exercise. 3:30 PM

10

11

12

13

14

15

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17

18

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25

26

27

A) Solve exercises p. 557 # 14-18 + p. 559 # 3-7 B) Study for the true/false quiz on Tuesday. Especially review important results, theorems (IVT, MVT, Rolle, etc...) and their consequences. 8:30 AM

28

29

Solve p. 449 # 9-20. Use either guess and check or the addition technique. 8:30 AM

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31