APPM1360Spring07Test3

APPM1360Spring07Test3 - X n = 1 (-2 ) n n ( x + 3 ) n 3....

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Exam #3 APPM1360 Spring 2007 ON THE FRONT OF YOUR BLUEBOOK write: (1) your name, (2) your student ID number, (3) lecture section (4) your instructor’s name, and (5) a grading table. You must work all of the problems on the exam. Show ALL of your work in your bluebook and box in your final answer. A correct answer with no relevant work may receive no credit, while an incorrect answer accompanied by some correct work may receive partial credit. Text books, class notes, and calculators are NOT permitted. Maximum score: 105 points. Question 1 : 18 points, Question 2 : 16 points, Question 3 : 20 points, Question 4 : 30 points, Question 5 : 16 points 1. (a) Using only series and their properties evaluate the limit lim x 0 e x - e - x x (b) Find the function with Mclaurin series X n = 1 nx n - 1 2. Find the radius and interval of convergence of the series
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Unformatted text preview: X n = 1 (-2 ) n n ( x + 3 ) n 3. (a) Write f ( x ) = x ( 1-x ) 2 as a power series. (b) Substitute x = 1 2 in your answer in part (a) and thus, or otherwise, nd X n = 1 n 2 n . 4. Consider the function f ( x ) = cos ( x ) . (a) Find the Mclaurin series of f ( x ) . (b) If f ( x ) is approximated by 1-x 2 estimate the error in the integral Z 1 cos ( x ) d x . (c) Calculate the exact value of Z 1 cos ( x ) d x . You may use the substitution x = u 2 . 5. Classify the equation for the di erent values of c given below. You must explain your reasoning. x 2 15-c-y 2 c-6 = 1 ( a ) 6 < c < 15, ( b ) c < 6, ( c ) c > 15. Extra credit ( 5 points ): If f ( x ) = sin ( x 3 ) nd f ( 15 ) ( ) . Good Luck!!!...
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This note was uploaded on 05/01/2008 for the course APPM 1360 taught by Professor Lim,jisun during the Spring '06 term at Colorado.

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