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Some past exams of Calculus for students. Keywords of the exam are: Series, Convergence, Determine, Comparison Test, Improper Integrals, Integral Converges, Diverges, Interval and Radius, Convergence of the Series, Drug
Typology: Exams
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Name:
Show all your work to receive full credit for a problem.
There are six questions. Questions are printed on both sides of a page.
(a)
∑^ ∞
n=
2 n − 1 n^3 + n + 8
(b)
∑^ ∞
n=
n^2 − 5 n^2 + 1
(a) Use the comparison test for improper integrals to decide if the integral converges or diverges. ∫ (^) ∞
1
xe−x x + 1
dx.
(b) Determine the convergence of the following series.
∑^ ∞ n=
ne−n n + 1
(a) How much of the drug will be in your body immediately after the first dose? after the second dose? Write an expression for the amount of drug in your body immediately after the nth dose.
(b) If you keep taking the drug forever, will the amount of drug in your body immediately after each dose level off? If so, what will this level be? If not, explain why not.
(a) the x-axis
(b) the y-axis
