Question

$f\left(x\right)=\frac{3x^2+ax+a+1}{x^2+x-2}$ and $\underset{x\to -2}{lim}f\left(x\right)$ exists.

Then the value of $(a-4)$ is?

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

The correct option is A $9$

$f\left(x\right)=\frac{3x^2+ax+a+1}{(x+2)(x-1)}$
As $x\to -2,D^r\to 0$. Hence, as $x\to -2,N^r\to 0$. Therefore,
$\therefore 12-2a+a+1=0$ or $a=13$
Hence, option 'A' is correct.