Mathematics - Area Under Curves Question with Solution | TestHub

$f(x)=\frac{-e^x+2^x}{x}$ $=\frac{1}{x}[-\left(1+\frac{x}{1!}+\frac{x^2}{2!}+\frac{x^3}{3!}+..\right)+1+\frac{\log 2}{1!}x+$ $\frac{(\mathrm{bg}2{)}^2}{2!}{x}^2+\frac{(\log 2{)}^3}{3!}{x}^3+..]$ $\begin{array}{rl}\mathrm{f}(\mathrm{x})=& \log 2-1+\frac{\mathrm{x}}{2!}\left\{(\log 2{)}^2-1\right\}\\ & +\frac{{\mathrm{x}}^2}{3!}\left\{{\left({\log }^2\right)}^3-1\right\}+\dots .\end{array}$ Putting $x=0$, we get $\mathrm{f}(0)=\log 2-1+0+0+\dots .=-1+\log 2$