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Unformatted text preview: MATH 2250 PRACTICE SHEET FOR FINAL EXAM 1. Use the definition of the derivative to find the derivative of the function f ( x ) = x 2 + 1 2. Use the definition of the derivative to find the derivative of the function f ( x ) = x + 1 x 3. Find an equation for the tangent line to the graph of the function f ( x ) = e x 3 x + ln x at x = 1. 4. Compute the following limit lim x → 3 e x e 3 x 3 5. Compute the following limit lim x → 3 e x e 3 x 6. Find the absolute minimum and maximum values of the function f ( x ) = x + ln x on the interval [1 ,e ]. 7. 8. Consider the function f ( x ) = 3 1 + x 3 , and suppose that F ( x ) is an antiderivative for f ( x ) with F (0) = 0. a. Explain why F ( x ) = Z x 1 1 + t 3 dt b. Use Rolle’s Theorem to show that there is at most one solution to the equation F ( x ) = 1. c. Write an equation for the tangent line to the graph of F ( x ) at x = 0 d. Use linear approximation to estimate the value of F ( 1 20 ) 1 9. Suppose that we have functions x (...
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This note was uploaded on 12/10/2011 for the course MATH 2250 taught by Professor Chestkofsky during the Spring '08 term at UGA.
 Spring '08
 CHESTKOFSKY
 Calculus, Derivative

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