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Unformatted text preview: R around the y-axis. 3) Suppose f ( x ) = x-ln x . a) Verify that lim x + f ( x ) = 0 and lim x f ( x ) = 0. Graph f on the interval [0 , 10]. b) A remarkable result of third semester calculus is that R - e-x 2 dx = . Assume that this result is correct, and use it to show that R x-ln x dx = e 1 / 4 . ( Maple can do the rst integral, but not the second!) Hint Make a change of variables, and then complete the square. c) Include a graph of e-x 2 on the interval [-2 , 2]. Use your answer to b) to compare this graph to the graph in a)....
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This note was uploaded on 02/29/2012 for the course MATH 152 taught by Professor Sc during the Fall '08 term at Rutgers.
- Fall '08