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The spring 2005 calculus ii exam for math 121 students. The exam covers topics such as derivative evaluation, integral evaluation, function properties, logarithmic properties, and area calculations. It is a closed-notes and closed-book exam with no calculators allowed.
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Test #3 Name: Hour 9AM 10AM 11AM Instructor:
This exam is CLOSED NOTES and CLOSED BOOK. There are NO CALCULATORS allowed. To get full credit you must show all work neatly in the space provided on the test paper.
a.
d dx
( 1 ln(x^2 + 1)
)
b. f ′(0), where f (x) = e−x(3 sin(x) + 2 cos(x))
c. f (x) = ex^ arctan(x)
d. f ′(1/2), where f (x) = arcsin(
x)
a.
∫ (^) e
1
1 + x x^2
dx
b.
∫ (s + 1) cos(s es) es^ ds
c.
∫ (^) sin(t)
5 + cos^2 (t)
dt
d.
∫ (^) dx
x
√ 1 − (ln(x))^2
e^4 x^5 √ x^3 + 2
as an equivalent expression in terms of
sums and differences of logarithms, in simplest terms.
b. For the function f (x) determined by your answer to (a), give the exact numerical values f (0), f (2), and f (4).
b. Find the area of that region.
