a. Let f(x) = frac{e^{x}-e^{-x}}{x} text{Find} lim_{x rightarrow 0}(e^{x}-e^{-x})/x

Question

a. Let

f (x) = \frac{e^{x} - e^{- x}}{x}

Find lim_{x \to 0} (e^{x} - e^{- x}) / x

Answer 1

The given function is, $f (x) = (e^{x} - e^{- x}) / x$
Note that, the given function is of the form $\frac{0}{0}$ .
Now, apply L hopital’s rule and obtain the value of the limit as shown below.
$lim_{x \to 0} f (x) = lim_{x \to 0} \frac{\frac{d}{d x} (e^{x} - e^{- x})}{\frac{d}{d x} (x)}$
$lim_{x \to 0} f (x) = lim_{x \to 0} \frac{e^{x} + e^{- x}}{1}$
$lim_{x \to 0} f (x) = 2$
Thus, the value of $lim_{x \to 0} f (x) = 2$ .

a. Let f(x) = frac{e^{x}-e^{-x}}{x} text{Find} lim_{x rightarrow 0}(e^{x}-e^{-x})/x

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