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Unformatted text preview: Practice problems for Test 1 September 18, 2008 1. Evaluate the limit, if it exists: lim t → ( 1 t 1 t 2 + t ) 2. Use the definition of a derivative to find f ( x ) and f 00 ( x ) given f ( x ) = 1 x 3. Differentiate the function using the rules y = sin θ 2 + c θ . 4. Let f ( x ) = 6 x 2 . Find f ( x ) using definition of derivatives. 5. Find lim x →∞ ( √ x 2 + 6 x √ x 2 + 9 x ). 6. Find lim x →∞ x 2 + x 3 +6 x 5 1 x 3 +8 x 4 . 7. Find the limit if it exists lim x → 2 (2 x +  x 2  ) 8. Use the intermediate value theorem to show that there is a root of the given equation in the specified interval sin ( π x ) = x , (0 , 1) 9. Find the limit lim x →∞ ( x 5 + x 6 ) 10. For what xvalues is f ( x ) continuous? f ( x ) = x +2 x 2 x 6 11. Use limits to compute the derivative of f ( x ) = √ 3 x at x = a . Use your result to give the equation of the tangent line to the graph of f ( x ) at x = 1, written with y as a function of x ....
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This note was uploaded on 09/28/2008 for the course MAT 265 taught by Professor Lin during the Spring '08 term at Foothill College.
 Spring '08
 lin
 Calculus, Derivative

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