408CF09assign8 - 2 and y = 4 Find the volume of the solid...

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M408C Fall 2009 Assignment 8 Due Thursday, November 5 You should have read and understood sections 6.2, 7.1, and 7.2* before completing this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. The base of a solid is the region bounded by the curves y = x
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Unformatted text preview: 2 and y = 4. Find the volume of the solid given that cross sections perpendicular to the y axis are equilateral triangles. 2. Let R be the region bounded by the lines y = x , y = 2 x , and y = 4. Find the volume of the solid obtained by rotating R about the line y = 4. 3. Let f ( x ) = √ x 2 + 2 x , for x > 0. Show that f is one-to-one on the given domain and find the inverse of f . 4. Use logarithmic differentiation to find the derivative of f ( x ) = v u u t x 3 sin x (1-cos x )( x 2 + 1) . 5. Find the integrals: (a) Z dx x (ln x ) 2 . (b) Z 4 1 1 √ x (1 + √ x ) dx ....
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This note was uploaded on 11/30/2010 for the course M 408c taught by Professor Mcadam during the Spring '06 term at University of Texas.

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