Question

T$\underset{x\to 0+}{\lim }$ $\left(x^{n}lnx\right),n>0$

• A. does not exist
• B. exists and is zero
• C. exists and is 1
• D. exists and is $e^{-1}$

Answer 1

Answer: (B)

$\underset{x\to 0+}{\lim }$$\frac{\ell nx}{\frac{1}{x^n}}\left(\frac{\infty }{\infty }\right).$ Applying LH rule
$\Rightarrow \underset{x\to 0+}{\lim }\frac{\frac{1}{x}}{\frac{-n}{x^{n+1}}}=0$