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Unformatted text preview: f (4) ( x ) = 24 x-5 . | ES n | M 4 ( b-a ) 5 180 n 4 2 7) (15pts) Choose ONE, and explain thoroughly: a) Explain the integral formula used in the Shell Method. Include a picture, a limit, a sum, the volume of a shell, and plenty of words in your answer. b) Prove the formula ln( ab ) = ln( a ) + ln( b ) using the denition of ln c) Use the formula for the derivative of f-1 and of ln( x ) to prove the derivative of e x is e x . 8) (15pts) Answer True or False: ln( xe 3 x ) = ln( x ) + exp(ln(3 x )) for all x > 0. log 2 3 log 3 4 = 2 Simpsons rule with n = 10 produces an exact answer for R 5 2 5 x 3 + 7 dx . R ln( x ) dx = x ln( x ) + x-C . The best approach to R sin 3 x cos 2 x dx is to set u = sin( x ). BONUS (5 pts; not supposed to be easy): Evaluate R 1 + e x dx by nding the correct u-substitution. You might try; u = e x , u = 1 + e x or u = 1 + e x . 3...
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- Summer '08