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A test review for calculus ii students, covering topics such as integrals, volumes, and limits. The review includes instructions for the test, as well as specific questions and problems to solve. Students are expected to answer all questions directly on the test and show their work. The document also includes problems related to sketching areas, finding points of intersection, setting up integrals, evaluating volumes, and computing limits.
Typology: Exams
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Name: Box #
Instructions
Question Possible Points Points Obtained 1 40 2 20 3 20 4 20 Total 100
1.a Sketch the area contained between the two curves
x^2 + 9y^2 = 9 x + y = 1
1.b Find all points of intersection between the two curves:
1.c Set up the integral(s) to compute the area between the two curves. You may integrate along either x or y axis:
1.d What is the area, to 4 decimal places. Say how you got the area.:
3 Compute these limits. Show all steps.
a
x^ lim→ 5
x^2 − 25 cos(x − 5) − 1 b
x^ lim→ 1
ln x x − 1 c
x^ lim→∞
x^3 + 3x e^2 x d
x^ lim→∞
ln x x^2 e x^ lim→∞ x^2 e−sx, s >^0
a (^) Z (^) ∞
0
t^2 e−stdt
b (^) Z (^1)
0
ln xdx
c (^) Z (^) ∞
1
xpdx, p > 1
d (^) Z (^) ∞
−∞
dx 1 + x^2
−∞
dx 1 + x^2
0
dx 1 + x^2 e (^) Z (^2)
0
dx (1 − x)^2
0
dx (1 − x)^2
1
dx (1 − x)^2
