HOMEWORK MATH 136

HW 1: Handout + 4.5 12,16,20,24,28
HW 2: 6.2* 16,18,20,24,26,28,40,68,70,72,74,76   
HW 3: 6.3* 32,34,36,38,40,42,46,50,80,82,84,86,88,90
HW 4: 6.4* 26,28,36,40,42,46,48,50
HW 5: 6.5 4,8,12,18   6.7  36,38,40,42,44,46,48,68,70,72
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HW 6: 6.6 22,26,32,36,62,64,66,68,70,72,74
HW 7: 6.8 12,14,16,18,22,24,26,28,38,44,48,52,54,56,58,64,66,70
HW 8: 7.1 10,14,16,20,22,26,32,38,40,44
HW 9: 7.2 2,10,14,16,18,22,28,30,34,38,44,48,54
HW 10: 7.3 10,14,16,20,26,28,34,36
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HW 11: 7.4 12,16,20,24,28,32,36
HW 12: Will count for Online also: 7.5 12,16,20,24,28,32,36,40,44,
48,52,56,60,64,68,72,76,80,84,88
HW 13: 7.7  8,12,20
HW 14: 7.8  6,8,10,14,18,22,24,30,32,34,38,40,42,44
HW 15: 8.1  10,14,16  10.1 8,10,14,18
HW 16: 10.2  6,10,22,36,38,48,50,58,60
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HW 17: 10.3  2ab,4ab,16,18,20,22,24,26,36,42
HW 18: 10.4  20,32,46,50,52,64,66
HW 20: 11.1  12,14,30,32,34,38,40,42,44,46,48,50
HW 21: 11.2  8,18,20,24,30,34,38,40,42,44,46,48,50,56
HW 22: 11.3  14,16,20,22,24,26,28,38just find s-10 and give a range for
the entire sum using s-10
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HW 23: 11.4  8,10,12,14,16,18,20,22,24,30,32,34,38,40
HW 24: 11.5  8,12,14,18,22,24,26,28,30,32,34,44
HW 25: 11.6  4,6,8,12,14,22,24,28,30
HW 26: Will count for Online also:  11.7 10,14,18,22,26,30,34,38,42,46
HW 27: 11.8 6,8,10,12,14,20,26,32
HW 28: 11.9  4,6,10,18,30,32,36
HW 29: 11.10  12,14,16,18,20,28,32,42,56,60,64 
the end

Questions:

1. How do we know the derivative of ln x is 1/x?
2. Draw a picture of ln 5.
3. Work out the integral of tanx.
4. Work out the integral of secx.
5. Describe the number e.
6. Describe the number e^5.
7. Show the derivative of e^x is e^x.
8. If A(t) stands for the amount at time t what does the formula
A'(t)=k A(t) mean in everyday terms?
9. What formula for A(t) makes A'(t)=k A(t) true?
10. What is sinh x?
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11. What is the restricted domain of sin x so it will have an inverse?
12. What is the restricted domain of cos x so it will have an inverse?
13. What is the restricted domain of tan x so it will have an inverse?
14. What is the restricted domain of sec x so it will have an inverse?
15. Workout the derivative of arcsin x.
16. Workout the derivative of arccos x.
17. Workout the derivative of arctan x.
18. Workout the derivative of arcsec x.
19. What theorem from Calculus I is used to prove l'hopitals rule?
20. Integration by Parts comes from what differentiation rule?
21. In trig-sub why is it ok for example that SQRT(cos^2 theta) = cos theta?
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22. The Trapezoid Rule approximates the area by doing what with ____
consecutive slice points?
23. Simpson's Rule approximates the area by doing what with ____ 
consecutive slice points?
24. The Trapezoid Rule is perfect on what kind of functions?
25. Simpson's Rule is perfect on what kind of functions?
26. Different parametric equations always give a different curve in 
the plane.  T or F
27. The formula for arc length was found by getting what kind of sum?
28. Why is dy/dx = (dy/dt)/(dx/dt)
29. Why worry about approximating definate integrals?
30. What theorem is used to prove the error formulas for Simpson's Rule, Trapezoid Rule and
Midpoint Rule?
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31. The formula for area in polar coordinates we divided into not little 
almost rectangles, but little almost _________ and came out with what 
kind of sum?
32. How did we get the formula for arc length with polar coordinates? We
___________ x & y in terms of _______
33. How did we get the formula dy/dx = (dr/dtheta * sin theta + r cos theta)
/(dr/dtheta * cos theta - r sin theta)?  We ____________ x & y in terms of
________ and used dy/dx = (dy/dt)/(dx/dt).
34. Using polar coordintes one could think of parametrizing x & y in terms 
of theta how?
35. If An=f(n) and f(x) goes to L as x goes to infinity, then the sequence
An also goes to _____ because we are just concerned about (what kind of 
numbers?) and when we say f(x) goes to L we mean for (what kind of numbers?)
36. If An goes to 0 what does that mean about the SUM An?
37. If An does not go to 0 what does that mean about the SUM An?
38. A sequence that is increasing and bounded above does what?
39. A series is a sequence, namely a sequence of __________ _____
40. A GS converges only if r is what? And if it converges it converges to 
what?
41. A P-series converges only if p is what?
42. Integral test needs what 3 things to work?
43. In the Integral Test if the integral converges we can see that the
partial sums have what two properties making them converge?
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44. In the DCT if one series converges and the other series has smaller
terms then the other series has what two properties making them converge?
45. The proof of the LCT uses what test in its proof.
46. In the AST we showed the even partial sums _______ and the odd partial 
sums __________, we also showed the even partial sums have what other 
property?
47. The proof of the root test and the ratio test end up comparing the 
series with what kind of series?
48. In the alternating harmonic series if you rearrange the order of the
terms what sum will you get?
49. What is the sum of the alternating harmonic series in regular order?
50. What is the sum of the p-series for p=2? and who showed that?
51. Intuitively we think of power series as __________ with degree _____.
52. Do all functions have power series?
53. What is another name for the Taylor Polynomial of degree 1 at x=a for 
f(x)?
54. If a function has a power series, will that power series converge
to the function?
55. What is the purpose of Taylor's Theorem aka Taylor's Inequality?