review 4f10 - MAC 2311 Test Four Review Fall 2010 Exam...

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MAC 2311 Test Four Review, Fall 2010 Exam covers Lectures 28 { 34, Sections 4.7 - 5.4: omit lecture 29, Section 4.8 1. Evaluate each integral: a. Z ( p x + 1) 2 p x dx b. Z cos x + sec x cot x dx c. Z csc ± csc ± ± sin ± (Hint: multiply each term in the fraction by sin ± .) d. Z 0 ± 1 = 2 3 ± 4 p 1 ± x 2 dx e. Z 1 = p 3 0 x 2 ± 1 x 4 ± 1 dx 2. True or false: a. If f ( x ) = e x= 8 , then Z f ( x ) dx = 8 f ( x ) + C . b. Z x 1 g 0 ( t ) dt = d dx Z x 1 g ( t ) dt c. Z f ( x ) g ( x ) dx = ±Z f ( x ) dx ²±Z g ( x ) dx ² 3. The slope of the tangent line to the curve y = f ( x ) at any point is given by x 3 + 3 p x x 2 . If f (1) = 0, ±nd the function f ( x ). 4. Evaluate each integral: a. Z e 1 d dx ( x ln x ) dx b. Z 1 ± 1 1 x 2 dx 5. Find the area under the graph of f ( x ) = ( cos x + 1 x < 0 2 e ± x x ² 0 on [ ± ² 2 ; ln 4]. 6. Find f ( e ) if f 00 ( x ) = 2 x 2 , f 0 ( ± 2) = 3 and f (1) = 2. 7. Find the maximum and minimum values of f ( x ) = xe ± x on [0 ; 3] and use them to ±nd upper and lower bounds for the de±nite integral Z 3 0 xe ± x dx . 8. If g ( x ) = Z x 1 [(ln t ) 2 + 2 t ] dt , ±nd g 0 ( e ). On what intervals is g ( x ) increasing and decreasing?
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This note was uploaded on 07/15/2011 for the course MATH 2311 taught by Professor T during the Spring '11 term at University of Florida.

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review 4f10 - MAC 2311 Test Four Review Fall 2010 Exam...

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