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November 24, 2014

November 24, 2014

Posted by **Steven** on Sunday, March 18, 2007 at 11:44am.

The Taylor series about x=5 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=5 is given by f^(n) (5)= (-1)^n(n!)/((2^n)(n+2)), and f(5)=1/2.

Write third degree Taylor polynomial for f about x=5. Then find the radius of convergence of the Taylor series for f about x=5.

I appreciate your help! Thanks

Do you mean the "nth derivative" or the "nth term in the (first)derivative"? of f(x)? It looks like you have written the coefficient of one term in a Taylor series, without the x^n term coefficient that should accompany it.

x=2

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