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short3a - (a Which one is it(b If it converges compute the...

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Exam 3a M175-001 Fall, 2009 Name: (1 pt.) 1. (10 pts.) Consider the sequence a n = n + 3 2 n - 1 ; n 0 (a) Graph the first six terms of the sequence on the axes provided below. Be sure that your axes are properly labeled. (b) Compute lim n →∞ a n . 1
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2. (25 pts.) Determine if each of the following is convergent or divergent. CIRCLE YOUR ANSWER. You do not need to show work, but you cannot receive partial credit for a wrong answer unless I can see how you got your answer. (a) summationdisplay n =2 n - 1 n 6 + 2 n CONVERGENT DIVERGENT (b) summationdisplay n =5 n 2 + 2 ln n n 3 - 3 n 2 CONVERGENT DIVERGENT (c) summationdisplay n =0 3(9) n 10 n CONVERGENT DIVERGENT (d) summationdisplay n =0 2 n + 4 n n 3 n CONVERGENT DIVERGENT (e) summationdisplay n =0 n ! 2 n CONVERGENT
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Unformatted text preview: (a) Which one is it? (b) If it converges, compute the exact sum of the series. If it diverges, explain why. 4. (10 pts.) Find the radius of convergence of ∞ s n =2 n 2 (3 x + 2) n 2 n +1 5. (10 pts.) Express f ( x ) = x 3-2 x as a power series centered at 0. 6. (10 pts.) Find the quadratic approximation for f ( x ) = (1 + x ) 1 / 3 centered at 0. 7. (10 pts.) Find the ±fth order approximation of f ( x ) centered at 0, given that f (0) = 2 and the derivative of f is f ′ ( x ) = cos x 1 + x 2 2...
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