07pf - at x = 1(b Use the tangent line approximation at x =...

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34A Practice for Final Fall 2007 Instructor: Prof. Wei Bring blue book and stapler for the final! I will hold extra office hours Monday, Dec. 10, 9-11am, 12:30-1:30 at SH6503. Final: Tuesday, Dec. 11, 8-11am, covering Chapters 1-8, with emphasis on Chapters 7,8. Practice Problems 1. Find the derivative of the following functions. (a) f ( x ) = 3 x 2 + 2 e 3 x (b) f ( x ) = x 2 +1 x (c) f ( x ) = ( x + 2 a ) 2 (d) Is the function f ( x ) = 3 t 2 - 4 t - t 3 increasing or decreasing when t = 1? (e) Find a nonzero function f ( x ) such that f ( x ) - 4 f ( x ) = 0. 2. (a) What is the equation of the tangent line to f ( x ) =
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Unformatted text preview: at x = 1? (b) Use the tangent line approximation at x = 1 to f ( x ) = √ x to find √ 1 . 1. 3. Some element has a half life of 20 years, how long does it take until 1% of the element left? 4. Page 50, # (3.2.31) 5. Solve for x: a) 5 x = 3 · 9 x . b) ln x 2 = ln x . 6. For f ( x ) = x + x 2 , what’s the average rate of change of the function from 1 to 1 + h ? What’s the instantaneous rate of change at x = 1? 7. Page 145, # (8.12.6) 8. Page 150, # (8.13.16), (8.13.20)...
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