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Unformatted text preview: Exam 2 Math 408C Name Fall 2009 TA Discussion Time: TTH
You must show sufﬁcient work in order to receive full credit for a problem. Do your
work on the paper provided. Write your name on this sheet and turn it in with your work. Please write legibly and label the problems clearly. Circle your answers when
appropriate. No calculators allowed. 1. (14 points) Let f (as) = sin2 cc — x/5 sin 3:, 0 g cc S 7r. Find all critical numbers of
f and classify the local extrema.
a: 2. (14 points) Describe the concavity of the function f (x) = 2 4
x _ and ﬁnd the points of inﬂection (if any exist). 3. (14 points) Find all horizontal asymptotes of the piecewise function x/zc2—3a:+2
f(x)= ”3‘2
—\/£L‘2+JI+1,IL'>0 4. (14 points) Water is pouring into a cone whose height is 8 inches and radius of
the base is 2 inches. If the volume (measured in cubic inches) of the water in the , 3:30 reservoir at time t (measured in minutes) is given by V(t) — the rate at which the water level is rising after 1 minute has elapsed. (Volume of a cone of height h and radius of base 7' is V = %7T7"2h.) 5. (14 points) Find the point (or points) on the curve 3/ = 1 +x, —1 S a: g 4 closest
to the point (5,0) and the points (or points) that are farthest from (5,0). 6. (14 points) Find a function f satisfying f”(:c) = sinx + 225% — 5, f’(0) = 3, and
f(0) = 1. 7. (a) (8 points) Use 4 subintervals to ﬁnd upper and lower bounds for the area of
the region under the curve y = 1 + 4332, —1 g m S 1. 1
(b) (8 points) Approximate / 1 1 + 4x2dx by a Riemann sum with n terms. (You do not need to evaluate the limit if this Riemann sum.) 1
Bonus: (5 points) Evaluate /_11 + 4x2dx by ﬁnding the limit of the Riemann sum 1)1 2 1
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 Spring '06
 McAdam

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