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Evaluate the limit as x approaches 0 of (cosec x) raised to the power 1/log x:

1. 0
2. 1
3. 1/e
4. None of these

Correct answer: 1/e

Solution

ln(value)=ln(cosec x)/ln x = -ln(sin x)/ln x. As x->0+, ln(sin x) ~ ln x, so the ratio -> -1 and the limit is e^(-1)=1/e.

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