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Practice_Final_Version_1

# Practice_Final_Version_1 - out the test and state your...

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Math 166 Final Exam May 2, 2009 Exam is 8 pages plus cover page. Follow the instructions for each question. Show enough of your work that we can understand what you are doing. 1. Find the derivatives of the following functions (12 points) (a) f ( x ) = e x 2 - 5 x + 2 (b) g ( x ) = x 3 tan - 1 x (c) h ( x ) = ln x sin - 1 x

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page 2 2. Find the maximum and minimum values of f ( x ) = xe - 2 x on the interval [0 , 5] (8 points) 3. Find lim x 2 ln( x - 1) x 2 - 4 (6 points)
page 3 4. Find (6 points) (a) x + 2 x 3 + x dx (6 points) (b) 1 - x 2 dx

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page 4 5. Evaluate (8 points) 4 1 x ln x dx 6. Set up an integral to find the length of the parametric curve x = t 2 + 2 t , y = t 3 + t , (6 points) where - 1 t 2. You do not need to evaluate this integral.
page 5 7. Sketch the graph of the polar coordinate equation r = 2 + cos(3 θ ), labeling a few points on (8 points) the curve with the related values of θ . Set up an integral to find the area inside the curve. You do not need to evaluate the integral.

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page 6 8. Find lim n →∞ 2 n 2 + 1 2 - 5 n Show work!! (8 points) 9. Decide whether the series n =1 ( n !) 2 (2 n )! converges or diverges. (8 points)

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Unformatted text preview: out the test, and state your conclusion. page 7 10. Decide if the series ∞ X n =1 (-1) n n n 3 + 2 is absolutely convergent, is conditionally convergent, (8 points) or the series diverges. Say which test(s) you are using to show convergence/divergence, show your work in carrying out the test(s), and state your conclusion. 11. Find the Maclaurin series for f ( x ) = x 3-x (8 points) page 8 12. The function g is given by the Taylor series g ( x ) = ∞ X k =0 ( x-3) k ( k + 1)2 k (8 points) Find the interval of convergence for the Taylor series. ( Be sure to indicate which of the the end points, if any, are included in the interval! ) Bonus Find the length of the parametric curve x ( t ) = 1-t 2 1 + t 2 and y ( t ) = 2 t 1 + t 2 for-1 ≤ t ≤ 1. (8 points)...
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Practice_Final_Version_1 - out the test and state your...

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