mid1g - Math 125G - Spring 2002 First Mid-Term Exam April...

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Unformatted text preview: Math 125G - Spring 2002 First Mid-Term 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 hand-written 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 x-axis to create a solid of revolution. If the volume of the solid is , find p. 6 ...
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mid1g - Math 125G - Spring 2002 First Mid-Term Exam April...

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