Math 131
Exam 2 Answers
In #16, intermediate steps need not be shown Optional simplified forms are shown inside cfw_braces
October 22, 2008
1. [10%] 2. [10%]
d x131 + 2x8 + e = 131x130 + 2 8x7 + 0 dx
cfw_= 131x130 + 16x7
d d d sin(2x) + (sin 2x) e-x e-x
1. (3 x 4% = 12%)
(a) Use the Intermediate Value Theorem (IVT) to show that f(z) =
2:3 2m + 2 has a zero in the interval (3, 0).
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EXAM 2 SOLUTIONS
Question 1
(a) Let f (x) = 2ex x3 4x. Calculate f (x) for all x.
Solution:
f (x) = 2ex 3x2 4
(b) Find the equation of the tangent line to the graph of f where x = 0.
Solution:
f (0) = 2 0 0 = 2
f (0) = 2 0 4 = 2
Either of the following ar