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Key points of this past exam of Calculus are: Definite Integral, Evaluate, Indefinite Integral, Area, Region Bounded, Curve, Line, Determining, Points, Intersections
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EXAM II - MARCH 13, 2009
Instruction: Read each question carefully. Explain ALL your work and give reasons to support your answers. Advice: DON’T spend too much time on a single problem.
Problems Maximum Score Your Score
1
2 EXAM II - MARCH 13, 2009
1.(10 pts.)(a) Evaluate the indefinite integral ∫ (^) x 3 4 + x^2 dx.
(10 pts.)(b) Evaluate the indefinite integral ∫ (^) x (^2) + 3x + 1 x(x^2 + 1) dx.
4 EXAM II - MARCH 13, 2009
(10 pts.)(b) Let g(x) = ln x. Find the fourth-degree Taylor polynomial P 4 (x) for g(x) centered at x 0 = 1.
MATH106A,B CALCULUS II - PROF. P. WONG 5 4.(10 pts.)(a) Let f (x) = sin(2x). What is the maximum possible er- ror, according to Taylor’s theorem, committed by using the third-degree Maclaurin polynomial M 3 (x) to estimate f (x) for − 12 ≤ x ≤ 12?
(10 pts.)(b) Let
f (x) =
see graph below, if 0 ≤ x ≤ 4; 0 , otherwise. Find a for which f (x) is a probability density function. Justify your answer.
x
y
(^014)
a
