MATH 151 HW

 

1.1 2,6,28,30,32,36,38,42

1.3 32,42

2.1 4,6

2.2 6,8,18,22,26,28

2.3 2,4,8,16,20,22,28,36,42,48

2.4 2,4,6,20,30,42

2.5 4,18,38,48

3.1 6,8,10ab,16,22,24a,30,32,52

***********************************************

3.2 6,10,20,22,24,36,40

3.3 8,10,14,18,24,30,40

3.4 4,12,14,42,44,46

3.5 12,20,22,24,26,34,40,42

3.6 10,16,18,28,32ab

3.7 4,8,18,28

*********************************************

3.8 4,10,16,21,22,34,35,42

3.9 2,6,18,22,28,32,34

4.1  30,36,40,46,52,56

4.2  2,6,14,16,18

4.3  6,8,12,32,38

4.4  12,16,20,22,24,34,46,48

4.5  10,12,24,28,30,46,48

4.7 4,14,18,26,32,36

*********************************************

4.8 6,14

4.9 4,10,14,24,30,34,38,40

5.2 2,6,12,18,30,40,48,50

5.3 8,16,18,22,26

5.4 4,10,14,20,32,42

5.5 12,14,16,30,36,38

6.1  4,8,10,16,20

*********************************************

6.2  6,10,18,26

6.3  2,12,16,22,24

6.4  14

6.5  4

7.2*  16,18,28,64,68,70

7.3*  34,40,42,76,78,82

 

Questions

 

1.  What makes a math problem a calculus problem?

2.  What causes the most problems for most students in calculus?

3.  For the most part limit rules are hard or easy to believe?

4.  Most people would say the formal proofs of the limit rules are

surprisingly easy or hard?

5.  Explain to a non-calculus person what lim as x approaches a of 

f(x) = L means.

6.  Give the exaxt meaning of lim as x approaches a of 

f(x) = L.

7.  Explain how this exact definition in #6 can be understood with in

a gameshow context.

8.  Explain to a non-calculus person what it means that f(x) is 

continuous at a.

9. Give the exact definition of f(x) is continuous at a.

10. How might you explain what continuous means to a noncalculus

person.
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11.  Know why the definition of the derivative makes sense. 

12. How might you explain what differentiable means to a noncalculus

person.

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13. The linear approximation of f(x) near a is what?

14. If f(x) is a differntiable function, then f'(x) is a function of

how many variables?  What are they?

15. If f(x) is a differentiable function, then df is a function of how

many variables?  What are they?

16. State the Max-Min Theorem.

17. Give an example to show that you must have continuous in the 

Max-Min Theorem.

18. Give an example to show that you must have a closed interval in 

the Max-Min Theorem.

19. How might you explain what the MVT says to a noncalculus person.

20. What theorem is used to prove "if f' is + then f is inc"?

************************************************

21. What theorem is used to prove that two functions with the same

derivative differ at most by + C?

22. Know why the definition of the definite integral makes sense.  We drew a picture and told the story in class.

23. Explain how Newton’s method works to a non-calculus person.

24. State the FTC part I.

25. State the FTC part II.

26. Explain to a non-calculus person what the FTC says.

27. Can the FTC always be used to find a closed form when integrating?  

28. Can the FTC be used to integrate integral from 0 to 2 of e raised to the x^2?

29. What is the only way to find this number in 28?

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30. Find the integral of tan x.

31. What is ln x?

32. How do we know what the derivative of ln x is?