If $\lim _{x \rightarrow \infty}\left(e^{2 x}+e^x+x\right)^{\frac{1}{x}}=e^a$, then the value of $a$

Question

If $\lim _{x \rightarrow \infty}\left(e^{2 x}+e^x+x\right)^{\frac{1}{x}}=e^a$, then the value of $a$ is $\_\_\_\_$

Professor PC Thomas Classes · Answer

$L=\lim _{x \rightarrow \infty}\left(e^{2 x}\right)^{\frac{1}{x}}=e^2$