"Evaluate the following limits. limx→0sin⁡3xtan⁡4x" was answered by students like you

Ramsey

Answered question

2020-12-01

Evaluate the following limits.

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x}

Luvottoq

Skilled2020-12-02Added 95 answers

Evaluate the following limits.

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x}

To evaluate:

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x}

Solution:

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x}

On simplifying further, we get:

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x} = lim_{x \to 0} \frac{\frac{\sin (3 x)}{(3 x)} \times (3 x)}{\frac{\tan (4 x)}{(4 x)} \times (4 x)}

= lim_{x \to 0} \frac{\frac{\sin (3 x)}{3 x}}{\frac{\tan (4 x)}{(4 x)}} \times \frac{3 x}{4 x}

lim_{x \to 0} \frac{1}{1} \times \frac{3}{4}

= \frac{1}{1} \times \frac{3}{4}

= \frac{3}{4}

Result:

lim_{x \to 0} \frac{\sin 3 x}{\tan 4 x} = \frac{3}{4}

Jeffrey Jordon

Expert2022-04-01Added 2605 answers

Answer is given below (on video)

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