Question

Limits that lead to the indeterminate forms $1^{\infty },0^0,{\infty }^0$ can sometimes be solved taking logarithm first and then using L'Hõpital 's rule
Let $\underset{x\to a}{\lim }(f(x){)}^{g(x)}$ is in the form of ${\infty }^0$, it can be written as $e^{\underset{x\to a}{\lim }g(x)\ell nf(x)}=e^L$
where $L=\underset{x\to a}{\lim }\frac{\ell nf(x)}{1/g(x)}$ is $\frac{\infty }{\infty }$ form and can be solved using L'Hõpital 's rule.
$\underset{x\to \infty }{\mathrm{Lim}}\left[(\ln x{)}^{1/2x}+x^{1/x^n}\right]\forall n\in N-$

• A. 2
• B. 0
• C. $e^{1/2}$
• D. $e$

Answer 1

Answer: (A)

Correct answer is (a) 2