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Unformatted text preview: listed in the on the Schedule and exercise list sheet found on the ACE webpage. This will give you much needed practice. Hand in your solutions to the following problems. Hand in Maple lab # 2 along with this assignment. 1. Find a power series representation for the functions and determine the radius of convergence. (a) ln( x 2 + 4) (b) x 2 ( a 3-x 3 ) 2 1 2. Show that the function f ( x ) = n x n n ! is a solution to the differential equation f ( x ) = f ( x ) . 3. Use a power series to approximate the denite integral R 1 10 1+ x 1-x dx with error less than 10-5 . 4. Compute the Taylor series of sin( x ) centered at 2 . 5. Use series to evaluate the limit lim x x-arctan( x ) x 3 . 6. Find the Maclaurin series of f ( x ) = sinh( x ) and prove that it converges to f ( x ) for all x . (Note: if you do not know sinh( x ) , search for hyperbolic functions in the index of the book.) 2...
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