Question

\(\lim\limits_{x\rightarrow0}\dfrac{2x}{\sqrt{4x^2+x^3}}\)

Answer 1

\(\lim\limits_{x\rightarrow0}\dfrac{2x}{\sqrt{4x^2+x^3}}\)

\(=\lim\limits_{x\rightarrow0}\dfrac{2x}{x\cdot\sqrt{4+x}}\)

\(=\lim\limits_{x\rightarrow0}\dfrac{2}{\sqrt{4+x}}=\dfrac{2}{\sqrt{4+0}}=1\)

Answer 2

Không tồn tại do \(\lim\limits_{x\rightarrow0^-}\dfrac{2x}{\sqrt{4x^2+x^3}}\ne\lim\limits_{x\rightarrow0^+}\dfrac{2x}{\sqrt{4x^2+x^3}}\)