Question

\(\lim\limits_{x\rightarrow0}\dfrac{\sin x-\sqrt{3}\cos5x}{3x}\)

Answer 1

\(=\dfrac{1}{3}\lim\limits_{x\rightarrow0}\dfrac{sinx}{x}-\lim\limits_{x\rightarrow0}\dfrac{\sqrt{3}cos5x}{3x}=\dfrac{1}{3}-\lim\limits_{x\rightarrow0}\dfrac{\sqrt{3}cos5x}{3x}\)

Xét:

\(\lim\limits_{x\rightarrow0^+}\dfrac{\sqrt{3}cos5x}{3x}=\dfrac{\sqrt{3}}{0}=+\infty\)

\(\lim\limits_{x\rightarrow0^-}\dfrac{-\sqrt{3}cos5x}{-3x}=\dfrac{-\sqrt{3}}{0}=-\infty\)

\(\Rightarrow\lim\limits_{x\rightarrow0}\dfrac{\sqrt{3}cos5x}{3x}\) ko tồn tại nên giới hạn đã cho không tồn tại