WBJEE · Maths · Limits
\(\lim _{x \rightarrow 0^{+}}\left(x^{n} \ln x\right), n>0\)
- A does not exist
- B exists and is zero
- C exists and is 1
- D exists and is \(e^{-1}\)
Answer & Solution
Correct Answer
(B) exists and is zero
Step-by-step Solution
Detailed explanation
We have, \(\lim _{x \rightarrow 0^{+}} x^{n} \ln x\) \(=\lim _{x \rightarrow 0^{+}} \frac{\ln x}{x^{-n}}\) \(=\lim _{x \rightarrow 0^{+}} \frac{x}{-n x^{-n-1}} \quad\) [using L'Hospital's rule \(]\)…
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