Limits and Continuity

**Limits of Exponential and Logarithmic Functions**

The following results are useful in the evaluation of the limits of exponential and logarithmic functions:

$1.\underset{x\to 0}{\mathrm{lim}}\frac{{a}^{x}-1}{x}={\mathrm{log}}_{e}a,a0$

$2.\underset{x\to 0}{\mathrm{lim}}\frac{{e}^{x}-1}{x}=1$

$\mathrm{3\dots}$

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