Question:
\(\displaystyle \lim_{x \to 0} \left(\csc x\right)^{\frac{1}{\log x}}\) is equal to:
\(\displaystyle \lim_{x \to 0} \left(\csc x\right)^{\frac{1}{\log x}}\) is equal to:
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Logarithmic limits are easier after taking \(\ln\).
Updated On: Apr 2, 2026
- \(0\)
- \(1\)
- \(\dfrac{1}{e}\)
- None of these
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Take logarithm: \[ \ln L=\frac{\ln(\csc x)}{\log x} \]
Step 2: As \(x\to0\), \(\csc x\sim \frac{1}{x}\).
Step 3: \[ \ln L=-1 \Rightarrow L=\frac{1}{e} \]
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