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 = √ π . Assume that this result is correct, and use it to show that R ∞ x-ln 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 e-x 2 on the interval [-2 , 2]. Use your answer to b) to compare this graph to the graph in a)....
View Full Document
- Fall '08
- Calculus, dx, small positive number