# Evaluate the following limits. lim_{xrightarrow0}frac{sin3x}{tan4x}

Question
Limits and continuity
Evaluate the following limits.
$$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}$$

2020-12-02
Evaluate the following limits.
$$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}$$
To evaluate: $$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}$$
Solution:
$$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}$$
On simplifying further, we get:
$$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}=\lim_{x\rightarrow0}\frac{\frac{\sin(3x)}{(3x)}\times(3x)}{\frac{\tan(4x)}{(4x)}\times(4x)}$$
$$=\lim_{x\rightarrow0}\frac{\frac{\sin(3x)}{3x}}{\frac{\tan(4x)}{(4x)}}\times\frac{3x}{4x}$$
$$\lim_{x\rightarrow0}\frac{1}{1}\times\frac{3}{4}$$
$$=\frac{1}{1}\times\frac{3}{4}$$
$$=\frac{3}{4}$$
Result: $$\lim_{x\rightarrow0}\frac{\sin3x}{\tan4x}=\frac{3}{4}$$

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