Solutions to Practice test 2

Solutions to Practice test 2 - SOLUTIONS TO PRACTICE TEST 2...

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Unformatted text preview: SOLUTIONS TO PRACTICE TEST 2 1. Find the limits: a) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 2 2 4 2 2 2 2 2 4 4 2 2 4 16 lim lim lim lim 2 4 32 2 2 2 x x x x x x x x x x x x x x x - +- + +- = = = + + =--- b) 3 1 lim 3 x x + = -- c) ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 1 1 1 1 1 1 1 1 1 lim lim lim lim 1 2 1 1 1 1 x x x x x x x x x x x x x x - +--- = = = + =--- + d) ( 29 5 5 3 2 2 2 3 2 lim lim lim 2 1 x x x x x x x x + + +- +- = =- = - + e) 2 2 2 4 4 4 4 3 3 3 5 2 5 2 5 5 lim lim lim lim 4 4 x x x x x x x x x x x + + + + + + = = = = + + f) 1 1 limsin / 2 x x - = 2. Use the graph to find: a) ( 29 1 lim x f x- - b) ( 29 4 lim x f x + 3. Is the function ( 29 3 2 , 1 2, 1 x x f x x x - = -- continuous at x = - 1? Explain, briefly, referring to the 3 part definition of continuity. Note that ( 29 ( 29 ( 29 3 2 3 1 1 1 1 1 lim 2 1; lim 1 x x f and x x +- - -- = - = -- = - = - so the 2-sided limit exists at 1 and = f( - 1), so f is continuous at 1. 4. Use the Intermediate Value Theorem to show that 4 5 x x-- = has a solution on [1, 2] Let ( 29 4 5 f x x x =-- This function is continuous since it is a polynomial. This function is continuous since it is a polynomial....
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This note was uploaded on 12/26/2011 for the course MAC 2311 taught by Professor Staff during the Fall '08 term at FIU.

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Solutions to Practice test 2 - SOLUTIONS TO PRACTICE TEST 2...

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