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Unformatted text preview: MAT 295 FINAL SPRING 2005 PRINT YOUR NAME
SIGNATURE
SOCIAL SECURITY NUMBER
INSTRUCTOR
LECTURE TIME READ THIS BEFORE YOU BEGIN This examination contains 8 problems for a total of 200 points. There are 8 pages in this
booklet. It is your responsibility to make sure that they are all present. Your solutions
must be written legibly and contain all the necessary steps which enabled you to arrive at
your answer in order to receive full credit. Unsupported answers will receive little credit. Do not write in the area below. 1. (40 pts) Evaluate each of the following limits if it exists. If it. does not exist explain
why. 2 — 6
(a) lim i.
z—+2 (C  2 (b) $13?) )2
 2
sm 32:
(C) Ill—IR) x2 W
(d) lim M z—roo 1‘2 +1 2. (40 pts) Find the derivatives of each of the following functions. You need not simplify
your answer. (a) f(:c) = (71:4 + a: +17)9. (C) f(:L‘) = xlnx. (d) f(3:) = tan2(:1:3 +1). 3. (10 pts) Let F(:r) :/ e‘/Z dt. Find F’(17).
0 1—$ 4. (10 pts) Let f(:1:) = 1+2: . Find f”(m). 5. (10 pts) If xyz + ysin(7m:) = 2 ﬁnd the equation of the tangent line to the curve at
(2, 1). 6. (30 pts) Carefully sketch and label the graph of the function f(:z:) = x4 — 4x3 + 10 by
using the information obtained in answering the following problems . (a) Find the intervals where f is increasing and decreasing and the location of all
local extreme values of f. (b) Find the intervals where f is concave up and concave down and ﬁnd all inflection
points of f. (c) Use the information in parts (a) and (b) [NOT YOUR CALCULATOR] to
sketch and label the graph of f. If your graph does not match the information in
parts (a) and (b) you will not receive any credit for this part. 7. (20 pts) A box with a square base and open top must have a volume of 32,000 cubic
centimeters. Find the dimensions of the box that minimize the amount of material
required to build it. 8. (40 pts) Find the following: (a) /(:r2 + 1)2dx. 7r/2
(b) / sinm(1+cosz)5dz:.
0 ...
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