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Unformatted text preview: Exam 2 (MODIFIED for 2009)
M175004
Spring, 2004 Name:
(1 pt.) 1. (15 pts.) Find the antiderivative. Show all steps. I need to know that your are doing the
work, not your calculator.
xe2x dx
2. (15 pts.) Find the antiderivative. Show all steps. I need to know that your are doing the
work, not your calculator.
x2
√
dx
4 − x2
3. (15 pts.) Find the antiderivative. Show all steps. I need to know that you are doing the work,
not your calculator.
x+1
dx
x2 − 2x
4. (15 pts.) Find n so that the error in a Trapezoid approximation to
√ π sin(x2 ) dx
0 is no more than 0.0001.
5. (20 pts.) Determine if each of the following is convergent or divergent. Reasons are not
required, but I will give no partial credit for a wrong answer with no reason.
∞ (a)
2 ∞ (b)
0 ∞ (c)
1 ∞ (d)
1 ∞ (e)
1 x2 + 3x − 1
dx
x4 + 2x
3x
2x+2
x ln x + 2
dx
x3 + x2
2x
xx
x(ln x)5
dx
ex 6. (10 pts.) Find a so that
∞
a dx
< 0.01
x(ln x)3 1 7. (10 pts.) Use the information below to approximate
∞
1 ln x + x
dx
ex with an error no greater than 0.002. f (x) = ln x + x
ex 2 3 4 5 2 Graph of the second derivative of 3 4 5 0 –0.2 –0.4 –0.6 –0.8 –1 –1.2 –1.4 Graph of the fourth derivative of
f (x) = ln x + x
ex 0 –2 –4 –6 –8 –10 2 ...
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 Fall '08
 STAFF
 Calculus, Exponential Function, Derivative, Logarithm, dx

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