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Unformatted text preview: f ( x ) g ( x ) for x a . If R a f ( x ) dx is convergent then R a g ( x ) dx is convergent. If R a g ( x ) dx is divergent then R a f ( x ) dx is divergent. Use the Comparison Theorem to determine whether the integral is convergent or divergent. You do not have to evaluate the integrals. You might have a look at Example 9 and Example 10 in Section 7.8 in the course textbook. (a) R 1 2+ e-x x dx Hint: Try to nd some relation between 2+ e-x x and 1 x for x 1. (b) R ( x 3 e-2 x ) dx Hint: Show that x 3 e-2 x e-x for suciently large x . You might use the fact that x 3 ln x for all x 5....
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This note was uploaded on 01/26/2012 for the course ECON 401 taught by Professor Burbidge,john during the Fall '08 term at Waterloo.
- Fall '08