MthT 430 Problem Set 12
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/(x
2
+ 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) = x
2
. Let h > 0. Compare f
¢
(0) with the
centered difference quotient at 0
:
f(0 + h)
-
f(0
-
h)
2h
.
·
Let f(x) = x
2
. Let h > 0. Compare f
¢
(a) with the
centered difference quotient at a
:
f(a + h)
-
f(a
-
h)
2h
.
·
Let g(x) = A x
2
+ 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
.
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On 28 Nov 2007, 21:52.