Question

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

Limits and continuity
ANSWERED
asked 2020-11-30

Use L'Hospital Rule to evaluate the following limits.
\(\lim_{x\rightarrow0}(\tan h x)^x\)

Expert Answers (1)

2020-12-01

Consider the given expression,
\(\lim_{x\rightarrow0}(\tan h x)^x\)
Since the function does not have any denominator hence, the L'Hospital rule cannot be applied.
Thus,
\(\lim_{x\rightarrow0^+}(\tan h x)^x=\lim_{x\rightarrow0^+}(\frac{e^x-e^{-x}}{e^x+e^{-x}})^x\)
\(=(\frac{e^0-e^{-0}}{e^0+e^{-0}})^0\)
\(=1\)
Which is the required value.

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