Evaluate the following limits. lim_{xrightarrow0}frac{tan5x}{x}

Question
Limits and continuity
asked 2021-02-22
Evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\tan5x}{x}\)

Answers (1)

2021-02-23
Given,
\(\lim_{x\rightarrow0}\frac{\tan5x}{x}\)
On simplification, we get
\(\lim_{x\rightarrow0}\frac{\tan5x}{x}=\lim_{x\rightarrow0}\frac{5\tan5x}{5x}\)
\(=5\cdot\lim_{x\rightarrow0}\frac{\tan5x}{5x}\)
\(=5\cdot\lim_{5x\rightarrow0}\frac{\tan5x}{5x}\ \ [\because As\ x\rightarrow0,5x\rightarrow0]\)
\(=5\cdot(1)\ \ [\because\lim_{\theta\rightarrow0}\frac{\tan\theta}{\theta}=1]\)
\(=5\)
0

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