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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 < = -≥ 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 δ ε , proof to show that 2 1 lim 2 1 2 x x → -=...
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- Spring '11
- Intermediate Value Theorem, English-language films, Continuous function, blue book