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Unformatted text preview: Math 115 -- Exam 1 Practice This exam is meant to suggest the kind, difficulty, and number of problems on the real exam. Note that topics covered in the course, but not included on this practice exam, still might appear on the real exam. Directions Set aside 90 minutes during which you can work on this exam without interruption. Refer to no books, notes, or calculators while working on the exam. This will give you a sense of your level of preparation for the real exam.
x2 1. Define f (x) by f (x) =
x 1 dt for -1 < x < 1. 1 - t3 d (a) Evaluate f (x). dx (b) Is f (x) increasing throughout its domain? 2. Consider the region pictured here, bounded by x = 0, x = 2, y = 0, and y = (x - 1)2 .
y 1 2 x (a) Find the volume when this region is rotated about the y-axis. (b) Set up the integral to find the volume when this region is rotated about the line y = -2. DO NOT EVALUATE THE INTEGRAL. 3. Suppose R is the region above the x-axis, below the line y = x + 1 and below the parabola y = 1 - x2 . (a) Sketch the region. (b) Find the area of the region. 4. Evaluate these integrals. (a) (b)
1 e3x+2 cos(e3x )dx
2 t2 dt t3 + 4 x2 + 1 dx. x2 + 3x + 2 1 x 9 - (ln x)2 ln(x2 + 1) dx. dx. 5. Evaluate the integral 6. Evaluate the integral 7. Evaluate the integral ...
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- Spring '08