Question

Answer 1

\(\lim\limits_{x\rightarrow0^+}f\left(x\right)=\lim\limits_{x\rightarrow0^+}\left(5ax^2+3x+2a+1\right)=2a+1\)

\(\lim\limits_{x\rightarrow0^-}f\left(x\right)=\lim\limits_{x\rightarrow0^-}\left(1+x+\sqrt{x^2+x+2}\right)=1+\sqrt{2}\)

Hàm có giới hạn \(x\rightarrow0\) khi \(2a+1=1+\sqrt{2}\Rightarrow a=\dfrac{\sqrt{2}}{2}\)