Question

If $f\left(x\right)=\{\begin{array}{c}\frac{x^2-(a+2)x+2a}{x-2},x\ne 2\\ 2,x=2\end{array}$ is continuous at $x=2$, then $a$ is equal to-

• A. $0$
• B. $1$
• C. $-1$
• D. $2$

Answer 1

The correct option is A $0$

$f\left(x\right)=\frac{x^2(a+2)x+2a}{x-2}$ , $x\ne 2$
$=2$ , $x=2$
is continuous at $x=2$
Applying L` Hospital's Rule
$\underset{x\to 2^{-}}{lim}f\left(x\right)=\underset{x\to 2^{-}}{lim}(2x-a-2)=2-a=2$

As it is continuous so we get $a=0$