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Main points of this exam paper are: Argument, Indicating, Converges or Diverges, Interval, Radius, Power Series, Determined, Endpoints, Planning, Compounded Monthly
Typology: Exams
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Name: ___________________________
Section (circle one):MWRF 11:00-11: MWRF 12:05-1:
Problem Possible Actual 1 14 2 12 3 12 4 12 5 12 6 12 7 10 8 10 9 6 Total 100
You must show all work to receive credit. Calculators are permitted. Give exact answers (ln 5, e^2 ) unless requested otherwise.
a) ) 10
1
∞
=
n n
∞
= +
1
8 6
n n n
n n
∞
= 1 (!)[( +^1 )!]
n n n
n
∞
=
n
n
n
n
x
. Be
sure to explain how you determined convergence or divergence at the endpoints.
0
2 e x^ dx. Give the first four non-zero terms.
b) What is the smallest number of terms you would need to use in order to compute this integral with an error of at most 10 −^7? Explain your reasoning
fraction.
b) What is the maximum possible error in your approximation? Explain your reasoning.
∞
= 1
n n^
diverges. If you make reference to any
integrals, you should compute their values and include an appropriate sketch. You may NOT simply say
∞
= 1
n (^) np
converges for p>1.
what is the maximum possible error in your estimate? You need not simplify numbers such as 210 or 10! in your answer. You may use the fact that e < 3.
