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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 !°1 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 ± ° cos 2 t 3. (20 points) Find the derivative of the following function using the limit
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