Solved Problems on Exponential Limits
First, recall the main formulas in the context of exponential/logarithmic limits. They will be widely used in the problems below: Formula 1. $\lim\limits_{x \to 0} \dfrac{e^x-1}{x}=1$ Formula 2. $\lim\limits_{x \to 0} \dfrac{\log_e(1+x)}{x}=1$ Formula 3. $\lim\limits_{x \to 0} \dfrac{a^x-1}{x}=\log_e a$ Exponential Logarithmic Limits: Problems and Solutions Problem 1: $\lim\limits_{x \to 0} \dfrac{e^{ax}-1}{x}$ Solution: Put $z=ax.$ Then … Read more