Solved find Taylor series expansion of log((1-x^2)^(1/x)) about x=0
Question : Find Taylor series expansion of the following function \[f\left(x\right)=Log{\left(\sqrt[x]{1-x^2}\right)}\] about x=0 Solution : \[f\left(x\right)=Log{\left(\sqrt[x]{1-x^2}\right)}\] \[f\left(x\right)=Log{\left(1-x^2\right)^\frac{1}{x}}\] \[f\left(x\right)=\frac{1}{x}Log{\left(1-x^2\right)}\] To find Taylor series expansion of f(x) about x =0 We first…