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2(a)10 ptsState Taylor’s theorem.
5 ptsCompute the fourth Taylor polynomial off(x) =ex+e-x2around the pointx0= 0 evaluated atx.
5 ptsGive a bound for the error you’d commit by using your answer to part (b)to approximatef(0.1).
3(a)5 ptsSuppose you want to find a zeropof a functionf(x). Newton’s method isgiven bypn+1=g(pn), whereg(x) is given by:g(x) =x-f(x)f0(x)3(b)5 ptsWritegas its first (linear) Taylor polynomial plus the remainder term around