Question

T$\displaystyle\lim_{x \to 0+}$ $\left(x^{n} \,ln\, x\right), n > 0$

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

Answer 1

Answer: (B)

exists and is zero

Answer 2

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