MthT 430 Problem Set 12

In class November 28, 2007 - Turn in December 5, 2007

A typed paper is preferred, but a neat hand written paper is OK.

Group Work Rules:

•

You are encouraged to work together!

•

Away from the group, do your own neat write up of the problems.

•

Acknowledge the group members and any other person/resource you use.

1.

Differentiate - Do not simplify your answer.

•

y = sin(1/x)cos(ln([x/(x² + 4 x +4)]))

Extra Credit: What is the domain of the function?

•

f(x) = sin(cos(sin(2 x)))

2.

Spivak Chapter 10, Problem 6.

3.

Spivak Chapter 10, Problem 15.

4.

Approximation of the derivative. See also Spivak Chapter 9, Problem 22.

•

Let f(x) = x². Let h > 0. Compare f^′(0) with the centered difference quotient at 0 :

f(0 + h)− f(0 − h) 2h .

•

Let f(x) = x². Let h > 0. Compare f^′(a) with the centered difference quotient at a :

f(a + h)− f(a − h) 2h .

•

Let g(x) = A x² + B x + C be a quadratic polynomial. Let h > 0. Compare g^′(a) with the centered difference quotient for g at a :

g(a + h) − g(a − h) 2h .

---

File translated from T_EX by T_TH, version 4.04.
On 22 Aug 2014, 13:16.