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Unformatted text preview: P + 1 n =1 ( & 1) n x n n . (b) (5 points) Find the interval of convergence for the above series. 5. (10 points) Find the Taylor Polynomials of orders , 1 , 2 , 3 generated by f ( x ) = cos( x ) at x = & 4 . 6. (a) (8 points) Express the inde&nite integral R sin( x 2 ) dx as a power series. (b) (2 points) Express the de&nite integral R 1 sin( x 2 ) dx as a number series. 7. (a) (5 points) Consider the function f ( x ) = (1 & 1 2 x ) & 2 . Find the &rst 3 terms of its Binomial Series. (b) (5 points) Find its radius of convergence. 8. (10 points) Solve the following initial value problem: dy dx = x 2 e & y y (0) = 0 : 9. (10 points) Find the general solution of (1 + x 2 ) y + 2 xy = e x 10. (10 points). Find the length of the curve y 2 = ( x + 1) 3 from (0 ; 1) to (3 ; 8) . 2...
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 Fall '11
 c
 Calculus

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