Since $f(x)=\ln x$ And $g(x)=e^{x}$ Are Inverse Functions, We Know That $e^{\ln (1+x)}=1+x$

question 56

Essay

Since $f(x)=\ln x$ and $g(x)=e^{x}$ are inverse functions, we know that $e^{\ln (1+x)}=1+x$ for x > -1.Find the Taylor series for $e^{\ln (1+x)}$ using only up to the quadratic terms and show that the result is 1 + x.

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