"Evaluate the following limits. limx→0tan⁡5xx" was answered by our experts

Wierzycaz

Answered question

2021-02-22

Evaluate the following limits.

lim_{x \to 0} \frac{\tan 5 x}{x}

Nicole Conner

Skilled2021-02-23Added 97 answers

Given,

lim_{x \to 0} \frac{\tan 5 x}{x}

On simplification, we get

lim_{x \to 0} \frac{\tan 5 x}{x} = lim_{x \to 0} \frac{5 \tan 5 x}{5 x}

= 5 \cdot lim_{x \to 0} \frac{\tan 5 x}{5 x}

= 5 \cdot lim_{5 x \to 0} \frac{\tan 5 x}{5 x} [∵ A s x \to 0, 5 x \to 0]

= 5 \cdot (1) [∵ lim_{θ \to 0} \frac{\tan θ}{θ} = 1]

= 5

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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