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

facas9 2020-11-30 Answered

Use L'Hospital Rule to evaluate the following limits.
$lim_{x \to 0} (\tan h x)^{x}$

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bahaistag

Answered 2020-12-01 Author has 101 answers

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

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Jeffrey Jordon

Answered 2022-04-01 Author has 2027 answers

Answer is given below (on video)

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