Mathematics

Mathematics

Problem

For f(x)=exf(x)=e^{x} centered at a=0a=0, the value at x=0.2x=0.2 is approximated by its degree-nn Maclaurin polynomial. Given that ∣f(n+1)(c)∣≤e0.2|f^{(n+1)}(c)|\le e^{0.2} for 0≤c≤0.20\le c\le0.2, determine the least integer nn that guarantees the absolute error is less than 1.0×10−61.0\times10^{-6}.

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