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Unformatted text preview: M408D Midterm Exam 2 57075/80/85 October 14 I. Multiple Choice. One and only one answer. Mark your answers in parentheses. 5 points for each problem. 1. (c) The graph of f is shown. 1 2 3 4 54321 1 2 3 x y Which following series can be its Taylor series? (a) 1 . 6 . 8( x 1) + 0 . 4( x 1) 2 . 1( x 1) 3 + (b) 2 . 8 + 0 . 5( x 2) + 1 . 5( x 2) 2 . 1( x 2) 3 + (c) 2 . 8 + 0 . 5( x 2) 1 . 5( x 2) 2 + 0 . 1( x 2) 3 + (d) 3 . 1 + 0 . 8( x 3) . 4( x 3) 2 + 0 . 1( x 3) 3 + 2. (c) Which the parametric equations will describe the following curve ? x y (a) x = t 4 t + 1 , y = t 2 (b) x = sin2 t, y = sin( t + sin2 t ) (c) x = cos5 t, y = sin2 t (d) x = sin2 t 4 + t 4 , y = cos2 t 4 + t 4 1 3. (b) Let p ( x ) be a power series centered at 1. That is, p ( x ) = X n =0 c n ( x 1) n . Which following interval can be its interval of convergence? (a) [0 , ) (b) [0 , 2] (c) ( 2 , 0] (d) ( 2 , 2) 4. (d) For which of the following series is the Ratio Test inconclusive (that is, it fails to give4....
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 Fall '07
 Sadler

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