Exponential Limits Problems and Solutions

The functions in exponential notation are involved in limits problems. Firstly, we must learn the standard exponential limits formulas for evaluating the limits of the functions in which either exponential functions or power functions or combination of both types of functions are involved. Here is a worksheet with list of example exponential limits questions for your practice and also solutions in different possible methods to learn how to calculate the limits of exponential functions in calculus.

Evaluate $\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize \dfrac{e^x}{\Big(1+\dfrac{1}{x}\Big)^{x^2}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{e^x-e^{x\cos{x}}}{x+\sin{x}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize (1+\sin{x})^{\Large \frac{1}{x}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{(e^{-3x+2}-e^2)\sin{\pi x}}{4x^2}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \sqrt[x^3]{1-x+\sin{x}}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{2^x-1}{\sqrt{1+x}-1}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize {\Bigg(\dfrac{5x^2+1}{3x^2+1}\Bigg)}^\dfrac{1}{x^2}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{5^x+5^{-x}-2}{x^2}}$

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