Limits
Limits of the Form 0^0
Premium Question
Grade 11

Question:

$\lim_{x \to 0^+} (\sin x)^x$
(1) $0$
(2) $1$
(3) $\infty$
(4) does not exist

Step-by-Step Solution

Key Concept: Let $y = (\sin x)^x$. Then $\ln y = x \ln(\sin x)$. As $x \to 0^+$: $x \ln(\sin x) \approx x \ln x \to 0$ (since $x \ln x \to 0$). So $\ln y \to 0$ and $y \to e^0 = 1$.
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Correct Answer: (2)

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