What is \( \lim_{x \to 0} \frac{10^{\sin x} - 1}{\tan x} \) equal to ?
- A. 0
- B. 1
- C. \ln 10 ✓
- D. \log_{10} e
Correct Answer: C. \ln 10
Explanation
Using L'Hopital's rule, the derivative of the numerator is \( 10^{\sin x} \ln(10) \cos x \) and the denominator is \( \sec^2 x \). Evaluating at x = 0 gives \( \ln 10 \).
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