Question

tìm a để hàm số sau liên tục tại x = 6

\(f\left(x\right)=\left\{{}\begin{matrix}\dfrac{3x^2-23x+30}{x-6}\\a\end{matrix}\right.\) khi \(x\ne6\); x = 6

Answer 1

\(\lim\limits_{x\rightarrow6}f\left(x\right)=\lim\limits_{x\rightarrow6}\dfrac{3x^2-23x+30}{x-6}\)

\(=\lim\limits_{x\rightarrow6}\dfrac{3x^2-18x-5x+30}{x-6}\)

\(=\lim\limits_{x\rightarrow6}\dfrac{\left(x-6\right)\left(3x-5\right)}{x-6}=\lim\limits_{x\rightarrow6}3x-5=3\cdot6-5=13\)

\(f\left(6\right)=a\)

Để hàm số liên tục  tại x=6 thì \(f\left(6\right)=\lim\limits_{x\rightarrow6}f\left(x\right)\)

=>a=13