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Unformatted text preview: Math 125G  Spring 2002 First MidTerm Exam April 23, 2002 Name Section 1 2 3 4 5 6 7 8 Total 10 10 10 10 10 10 10 10 80 Complete all questions. You may use a scientific calculator during this examination. Other calculating devices are not allowed. You may use one handwritten 8.5 by 11 inch page of notes. Show all work for full credit. You have 80 minutes to complete the exam. 1. Is 1 2 1 x ln x  x2 an antiderivative of x ln x ? Explain. 2 4 2. Suppose f (x) = 2 + ex , f (0) = 3 and f (0) = 2. Find f (x). 3. Use the midpoint rule with n = 3 to approximate the integral
6 ln(sin x + 3) dx.
0 4. Solve the following equation for m:
1 0 f (x) dx  2 1 2 0 1 0 f (2x) dx  f (x) dx = m
1 0 f (x) dx 5. Find the derivative of each of the following functions.
x2 (a) g(x) =
2 sin(t2 + 3t) dt 3 (b) h(x) =
2 ln v dv sin v 6. Evalate the following integrals: (a) x2 x dx +1 1 (b)
1 (2  x)6 dx 7. Find the area of the region bounded by the curves y = x2  3 2 and y = 1 2  x2 . 8. Let p > 1. Suppose the region in the first quadrant bounded by y = x and y = xp is rotated about the xaxis to create a solid of revolution. If the volume of the solid is , find p. 6 ...
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 Spring '08
 Chen
 Math

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