$$ \lim_{x \to \infty}(1+4/x)^\sqrt{x^2+1} $$ is like
$$ \lim_{x \to \infty}(1+1/x)^x = e $$
I have replaced $\sqrt{x^2+1}$ by $x$ but I haven't got the expected result ($e^4$).
$$ \lim_{x \to \infty}(1+4/x)^\sqrt{x^2+1} $$ is like
$$ \lim_{x \to \infty}(1+1/x)^x = e $$
I have replaced $\sqrt{x^2+1}$ by $x$ but I haven't got the expected result ($e^4$).