2211Fall08Test1[1] - x c f x g x (C) [ ] 2 lim ( ) x c h x...

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2211 Fall 2008 Test 1 Name______________________________________ Show all necessary work in your blue book. Please use a different page for each complete problem. Incorrect or non-work will not receive credit. When finished, please place this question paper inside your blue book and turn it in. No calculator or notes or book allowed. (100 points) 1. (5 points each) Compute the following limits, if they exist: (A) 0 lim x x x (B) 0 sin(2 ) lim sin(3 ) x x x 2. (5 points each) Compute the following limits, if they exist: (A) 0 1 1 lim ( 1) x x x x - + (B) 2 1 3 lim 1 x x x x - - - 3. (5 points each) Compute the following limits, if they exist: (A) 2 2 4 5 4 lim 2 8 x x x x x - + - - (B) 0 1 1 3 3 lim x x x - + 4. (5 points each) Compute the following limits, if they exist: A) lim ( ) x f x π given sin( ) 0 ( ) 1 cos( ) 0 cos( ) x x f x x x x x < = - B) x x x 2 cot 3 lim 2 2 0 5. (2 points each) Given that lim ( ) 5, lim ( ) 0, lim ( ) 2 x c x c x c f x g x h x = = = - find: (A) [ ] lim ( ) ( ) x c f x g x - (B) [ ] lim ( ) / ( )
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Unformatted text preview: x c f x g x (C) [ ] 2 lim ( ) x c h x (D) 1 lim ( ) ( ) x c g x h x - (E) [ ] lim ( ) / ( ) x c g x f x 6. (10 points) 4sin( ) Let ( ) 2 x x f x x a x x &lt; = - Find all choices for a such that f is continuous on the interval , 2 2- 7. (10 points) Find all discontinuities of f ( x ) and label them as essential, removable, or infinite, given that f ( x ) = 2 x 2 x 3-2 x . 8. (10 points) Use the Intermediate Value Theorem to show that there is a solution of the given equation in the indicated interval. 5 2 2 2-=-x x [2,4] 9. (10 points) Find the derivative of ( ) 2 3 f x x =-using the limit definition of the derivative. 10. (10 points) Use an , proof to show that 2 1 lim 2 1 2 x x -=...
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This note was uploaded on 03/30/2011 for the course MATHMATICS 1101 taught by Professor Zhong during the Spring '11 term at Georgia State University, Atlanta.

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2211Fall08Test1[1] - x c f x g x (C) [ ] 2 lim ( ) x c h x...

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