L'hôpital's Rule

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Using L'Hôpital's rule, lim(x→0) (eˣ - 1)/x equals

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1. **Indeterminate Form Check**: As $x 	o 0$, $e^x - 1 	o 0$ and $x 	o 0$. Form is $0/0$.
2. **Apply L'Hôpital's Rule**: Differentiate the numerator and denominator independently.
   - Numerator derivative: $\frac{d}{dx}(e^x - 1) = e^x$.
   - Denominator derivative: $\frac{d}{dx}(x) = 1$.
3. **New Limit**: $\lim_{x 	o 0} \frac{e^x}{1}$.
4. **Final Evaluation**: $e^0 / 1 = 1 / 1 = 1$.

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L'hôpital's Rule

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