Mathematics - Functions Question with Solution | TestHub

The integrand is the derivative of $(x+1)e^{x^2}$, and $f(0)=1$, so $f(x)=(x+1)e^{x^2}$. This gives (A), $f(1)=2e$, and $\log \left(f(x{)}^{1/x}\right)=\ln (1+x)/x+x\to 1$, so the limit is $e$.