Unformatted text preview: R around the yaxis. 3) Suppose f ( x ) = xln 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 ∞∞ ex 2 dx = √ π . Assume that this result is correct, and use it to show that R ∞ xln x dx = e 1 / 4 √ π . ( Maple can “do” the ﬁrst integral, but not the second!) Hint Make a change of variables, and then complete the square. c) Include a graph of ex 2 on the interval [2 , 2]. Use your answer to b) to compare this graph to the graph in a)....
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 Fall '08
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 Calculus, dx, small positive number

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