132_Final_Review - Mth 132 Final Review p. 1 Disclaimer:...

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Mth 132 Final Review p. 1 Disclaimer: There may be types of problems on the final exam that are not found on this review sheet and there may be types of problems on this review sheet that are not on the final exam. 1. Compute each of the following limits. Answer with a finite number, or one of these symbols: , - , DNE (does not exist). a. 2 2 ) 3 ( lim 2 + + + + - x x x x b. 2 2 ) 3 ( lim 2 + + + - - x x x x c. x x x 2 lim 2 + -∞ d. 3 2 4 1 lim - - - + + x x x x x e. - 3 0 sin lim x x x x f. x x sin lim 2. Compute each of the following limits. Answer with a finite number, or one of these symbols: , - , DNE (does not exist). a. 2 2 3 1 2 lim x x x x + + b. 4 5 lim 4 - x x c. ) ( lim 2 h q h where + - = 1 3 ) ( 2 h h h q for for 2 2 h h d. ) ( lim 1 x g x where + + + = 2 2 3 2 ) ( 2 x x x x g for for 1 1 < x x e. x x x + + - 2 1 2 1 lim 2 3. Graph the following rational function. Include the graphs and equations of the asymptotes and dominant terms. a. 1 2 + = x x y b. 1 4 2 - - = x x y 4. Explain why the equation x x = cos has at least one solution. 5. Use the definition of the derivative to calculate the derivatives of the following functions. a. 4 2 ) ( 2 + - = x x x f b. x x f 1 ) ( = 6. Find the slope of the curve x x y 2 cos sin + = at the point 2 π = x . 7.
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This note was uploaded on 10/17/2011 for the course MTH 133 taught by Professor Staff during the Fall '08 term at Michigan State University.

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132_Final_Review - Mth 132 Final Review p. 1 Disclaimer:...

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