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Question

Question: \(\lim_{x \rightarrow 0}\frac{\sin 3x + \sin x}{x}\)=...

lim⁡x→0sin⁡3x+sin⁡xx\lim_{x \rightarrow 0}\frac{\sin 3x + \sin x}{x}=

A

13\frac{1}{3}

B

3

C

4

D

14\frac{1}{4}

Answer

4

Explanation

Solution

lim⁡x→0sin⁡3x+sin⁡xx\lim_{x \rightarrow 0}\frac{\sin 3x + \sin x}{x} = lim⁡x→0sin⁡3xx+lim⁡x→0sin⁡xx\lim_{x \rightarrow 0}\frac{\sin 3x}{x} + \lim_{x \rightarrow 0}\frac{\sin x}{x}

= lim⁡x→0sin⁡3x3x.3+lim⁡x→0sin⁡xx\lim_{x \rightarrow 0}\frac{\sin 3x}{3x}.3 + \lim_{x \rightarrow 0}\frac{\sin x}{x} = 1.3 + 1 = 4.