Practice Exam 3

# Practice Exam 3 - MIT OpenCourseWare http/ocw.mit.edu 18.01...

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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Fall 200 6

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18.01 Practice Exam 3 Problem 1. a) (10) Derive the trigonometric formula cos 2 x = 1 2 sin 2 x and use it to evaluate sin 2 xdx . e b) (10) Diﬀerentiate x ln x , and use your answer to evalute ln x dx . 1 Problem 2. (15) K-mart is selling at half-price its left-over Great Pumpkins— thin orange plastic shells Flled with half-price Halloween candy. A Great Pumpkin has the shape of the curve x 2 + y 4 = 1, rotated about the vertical axis, i.e., the y -axis. This curve is symmetric about the x -axis and the y -axis it looks something like a circle, but somewhat ﬂatter at the top and bottom. Using units in feet, how many cubic feet of candy will it take to Fll a Great Pumpkin? Give the exact answer, then tell if 5 cubic feet will be enough. x
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## This note was uploaded on 10/10/2011 for the course MATH 31 taught by Professor Blake during the Spring '11 term at MIT.

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Practice Exam 3 - MIT OpenCourseWare http/ocw.mit.edu 18.01...

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