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Unformatted text preview: 4. Use power series to approximate Z . 1 1 1 + x 5 dx correct to within 10-5 of its true value. 5. Deﬁne J ( x ) = ∞ X n =0 (-1) n 2 2 n x 2 n ( n !) 2 (a) What is the radius of convergence of J ? (b) What is the interval of convergence of J ? (c) Show that J satisﬁes the diﬀerential equation x 2 J 00 ( x ) + xJ ( x ) + x 2 J ( x ) = 0 . 6. Find the taylor series of (a) cos( x 2 ) (b) xe-x (c) x ln(1-x 2 ) 1...
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This note was uploaded on 10/18/2011 for the course MATH V1102 taught by Professor Mosina during the Fall '08 term at Columbia.
- Fall '08