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Unformatted text preview: estimate. 2. Approximate Z 1 ln( x ) cos( x ) dx using Simpson’s rule with 4 intervals, and give an estimate on the error of your approximation. You can get around the problem of ln(0) cos(0) not being deﬁned as follows. First integrate by parts, and then it is reasonable to take sin(0) / 0 = 1 since lim x → sin( x ) x = 1. Similarly, you can use L’Hospital’s rule to determine that lim x → + ln( x ) sin( x ) = 0. So that you don’t kill yourself taking derivatives, I’ll tell you that the 4th derivative of sin( x ) /x is (( x 4-12 x 2 + 24) sin( x ) + (4 x 3-24) cos( x )) /x 5 , which is between-1 / 5 and 1 / 5 for any value of x ....
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This note was uploaded on 10/21/2010 for the course MAT 126 taught by Professor Sutherland during the Spring '07 term at SUNY Stony Brook.
- Spring '07