01_Final1-Sample

01_Final1-Sample - University of California, Riverside...

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Department of Mathematics Final Exam Mathematics 9A - First Year of Calculus Sample 1 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 ::: . (a) (6 points) lim x 3 x 3 9 x 6 + 2 x (b) (7 points) lim x ! 0 + sin(2 x ) x 2 (c) (7 points) lim x 3 x p 4 x 2 + x + 5 f ( x ) = ( x + 5 if x < 3 4 p x + 1 if x ± 3 (a) (6 points) Show that f ( x ) is continuous at x = 3 . (b) (14 points) Using the limit de&nition of the derivative, and com- puting the limits from both sides, show that f ( x ) is di/erentiable at x = 3 . 1
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01_Final1-Sample - University of California, Riverside...

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