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 18 01  Single Variable Calculus
Single Variable Calculus Documents

Geometric applications: volumes, area, arclength
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MIT OpenCourseWare http ocw mit edu 18 01 Single Variable Calculus Fall 2006 For information about citing these materials or our Terms of Use visit http ocw mit edu terms 18 01 Practice Exam 3 Problem 1 2 a 10 Derive the trigonometric formula cos 2x 1 2 sin x and use it to evaluate e b 10 Di erentiate x ln x and use your answer to evalute ln x dx sin2 xdx 1 Problem 2 15 K mart is selling at half price its left over Great Pumpkins thin orange plastic shells lled with half price Halloween candy A Great Pumpkin has the shape of the curve x2 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 atter at the top and bottom Using units in feet how many cubic feet of candy will it take to ll a Great Pumpkin Give the exact answer then tell if 5 cubic feet will be enough x 2 Problem 3 20 3 7 5 5 The function F x t2 e t dt is not elementary it comes up in 0 calculating the standard deviation of The Curve of normal distribution In the following a and b go together but c and d are both independent questions a Find F x b Find the critical point s of F x and determine their type s by studying the sign of F x when x is near a critical point 9 u c Express ue du in terms of values of F x 0 x3 if x 0 3 Problem 4 15 12 3 The end portion of a boneless AllSoy SmartHam of length a has approxi mately the shape of the region under the curve y x 0 x a rotated about the x axis d Estimate F x by showing that F x a When it is sliced vertically into thin slices what is the average area of a slice b Where on the SmartHam is there a slice having this average area i e how far from the tip Problem 5 15 7 8 You only have time to look at the newspaper on Sunday but the rst thing you turn to is the baseball statistics from Saturday s game to see how many hits your favorite ball player Pepe LeMoko got In September which started on a Saturday he had a slump in the middle but came out of it His record on
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