This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: f (4) ( x ) = 24 x5 .  ES n  ≤ M 4 ( ba ) 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 deﬁnition of ln c) Use the formula for the derivative of f1 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 Simpson’s rule with n = 10 produces an exact answer for R 5 2 5 x 3 + 7 dx . R ln( x ) dx = x ln( x ) + xC . 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 ﬁnding the correct usubstitution. You might try; u = e x , u = 1 + e x or u = √ 1 + e x . 3...
View
Full Document
 Summer '08
 Storfer
 Calculus, Shell Method

Click to edit the document details