Unformatted text preview: f ( x ) = x 4 x + 1 5. Evaluate the indeﬁnite integral as a power series.What is the radius of convergence? Z arctan( x 2 ) dx 6. a ) Show that the function f ( x ) = ∞ X n =0 x n n ! is a solution of the diﬀerential equation f ( x ) = f ( x ) b ) Show that f ( x ) = e x . 7. Find the sum of each of the following series. a ) ∞ X n =2 n ( n1) x n ,  x  < 1 b ) ∞ X n =2 n 2n 2 n c ) ∞ X n =1 n 2 2 n 1...
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 Spring '10
 Tor
 Math, Calculus, Power Series, lim cn xn

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