# Use L'Hospital Rule to evaluate the following limits.lim_{xrightarrow0}(tanh x)^x

Use L'Hospital Rule to evaluate the following limits.
$\underset{x\to 0}{lim}\left(\mathrm{tan}hx{\right)}^{x}$

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bahaistag

Consider the given expression,
$\underset{x\to 0}{lim}\left(\mathrm{tan}hx{\right)}^{x}$
Since the function does not have any denominator hence, the L'Hospital rule cannot be applied.
Thus,
$\underset{x\to {0}^{+}}{lim}\left(\mathrm{tan}hx{\right)}^{x}=\underset{x\to {0}^{+}}{lim}\left(\frac{{e}^{x}-{e}^{-x}}{{e}^{x}+{e}^{-x}}{\right)}^{x}$
$=\left(\frac{{e}^{0}-{e}^{-0}}{{e}^{0}+{e}^{-0}}{\right)}^{0}$
$=1$
Which is the required value.

Jeffrey Jordon