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Limits
L'Hôpital's Rule
Premium Question
Grade 11

Question:

$\lim_{x \to 0} \frac{a^x - b^x}{x}$
(1) $\ln(a/b)$
(2) $\ln(ab)$
(3) $ab$
(4) $a - b$

Step-by-Step Solution

Key Concept: By L'Hôpital (or definition of derivative at $x = 0$): $\left. \frac{d}{dx}(a^x - b^x) \right|_{x=0} = \ln a - \ln b = \ln(a/b)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)

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