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The final exam for ma 166 calculus course held in spring 2000. The exam consists of 25 multiple-choice problems covering various topics in calculus such as limits, derivatives, integrals, and series.
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MA 166 FINAL EXAM Spring 2000 Page 1/
x, x 2 , 0
, and C = (1, 2 , 0), where x > 0. If the area of the triangle is 6, then x = A. 4 B. 8 C. 3 D. 5 E. 2
A. 2 B.
x sin x 1 − cos^3 x
E. does not exist
1
1 + x^2 dx =
A. π 2 B. integral diverges C. π D. π 3 E. π 4
1
x ln xdx =
A. 2 ln 2 −
B. ln 2 −
ln 2 −
E. 2 ln 2 −
2
x^2 − 1
dx =
ln 3
B. ln
C. ln
ln
E. ln 3
A. π 2 B. π^2 C. π
D. π^2 2
E. π^2 3
x (^32) , 0 ≤ x ≤ 2, is equal to
A. 3
(I)
n=
(−1)n^ ln n n
n=
cos
n
n=
n^2 2 n
A. (II) and (III) only B. (III) only C. (I) and (II) only D. (I) only E. (I) and (III) only
(I)
n=
(−1)n^
n
n=
cos n n^2
n=
(−1)n^
n^3 + 1
A. (II) and (III) only B. (III) only C. (I) and (II) only D. (I) only E. (I) and (III) only
n=
3 n 7 n+
A. diverges
n=
ln n + 3n A. converges by comparison with
n=
ln n
B. diverges by comparison with
n=
ln n
C. converges by comparison with
n=
3 n
D. diverges by comparison with
n=
3 n E. diverges by the ratio test
n=
n^2 n!
xn^ is (^) A. e
B.
e C. 1 D. ∞ E. 2
0
e−x
3 dx with error less than 0.01. The smallest number of terms of the series that are needed for this accuracy is A. 2 B. 3 C. 4 D. 5 E. 6
x =
t^3 , y =
t^2 + 3, 0 ≤ t ≤ 1
is A. 2
x about a = 2, the coefficient of (x − 2)^3 is
A. −