05_Final1-Sample

05_Final1-Sample - University of California, Riverside...

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University of California, Riverside Department of Mathematics Final Exam Mathematics 9A - First Year of Calculus Sample 5 Instructions: This exam has a total of 200 points. You have 3 hours. You must show all your work to receive full credit. You may use any result done in class. The points attached to each problem are indicated beside the problem. You are not allowed to use books, notes, or calculators. Answers should be written as p 2 as opposed to 1 : 4142135 ::: . 1. Find each of the following limits if it exists. If you think the limit does not exist provide a reason. (a) (5 points) lim x ! 0 sin (5 x ) 1 p 1 x (b) (5 points) lim t ! 9 + 5 t 3 p t (c) (5 points) lim x ! 8 f ( x ) ; given that lim x ! 8 xf ( x ) 3 = 2 (d) (5 points) lim x p 9 x 6 x 3 x 3 + 4 x 2. Find the derivative of the following functions: 1
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(a) (5 points) g ( ) = ± 2 (sec sin 2 ) 2 (b) (5 points) f ( x ) = x 2 (5 x ) 7 (c) (5 points) y = 1 2 p x 5 3 x cos (3 ± ) (d) (5 points) f ( t ) = tan t
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This note was uploaded on 01/11/2010 for the course MAT 9a taught by Professor Nouh during the Spring '09 term at UC Riverside.

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05_Final1-Sample - University of California, Riverside...

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