review 4f11 - MAC 2311 Test Four Review, Fall 2011 Exam...

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MAC 2311 Test Four Review, Fall 2011 Exam covers Lectures 26 { 33, except lecture 29 Online Calculus Text, Chapter 4 sec. 26 { 30, plus Chapter 5, sec. 31 { 33 (omit sec. 29) 1. Evaluate the following limits. Use L’Hospital’s Rule if it applies. a. lim x !1 ( e x + x ) 1 x b. lim x ! 0 + (cos x ) 1 =x 2 2. Find each horizontal asymptote of f ( x ) = x 2 e ± x . Use L’Hospital’s Rule if necessary. Then sketch the graph of f ( x ), showing all local extrema and in±ection points. 3. Let f ( x ) = x 2 ln x . Evaluate lim x ! 0 + f ( x ) and lim x !1 f ( x ), using L’Hospital’s rule if necessary. Then graph the function, showing all asymptotes, holes, intercepts, extrema and in±ection points. Note that f 00 ( x ) = 3 + 2 ln x . 4. Find the most general antiderivative of the following: (a) f ( x ) = ( p x + 1) 2 p x on (0 ; 1 ) (b) g ( x ) = cos x + sec x cot x on (0 ; ± 2 ) (c) f ( x ) = x 4 + x 2 ± 2 x 2 + 1 Hint: use long division to rewrite the function. 5. True or false: (a) If f ( x ) = e 6 x , then Z f ( x ) dx = 6 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 6. 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 .
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This note was uploaded on 02/14/2012 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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review 4f11 - MAC 2311 Test Four Review, Fall 2011 Exam...

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