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This is a question in Taylor series



4. (i) Let g(x) be an infinitely differentiable function. Find the linear and
quadratic Taylor approximations of es() around the point 0.
(ii) Use the result above to compute the quadratic Taylor approximation
around 0 of e(*+1)2
(iii) Compute the quadratic Taylor approximation around 0 of e(+) by using
Taylor approximations of e and ex.

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1 let flatze _ fixl= g/x )e" and f" ( x / = g" ( x ) 9
Hence the linear Taylor approximation is ( at x=0 )
f ( x ) = f (o ) + flox
= et goex
and the quadratic Taylor approximation...

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