Question

Let f(x) = $\{\begin{array}{cc}\frac{x^3+x^2-16x+20}{(x-2{)}^2},& ifx\ne 2\\ k,& ifx=2\end{array}.$ if f(x) be continuous for all x, then k =

• A. 7
• B. -7
• C. $\pm 7$
• D. None of these

Answer 1

The correct option is A 7

For continuous $\underset{x\to 2}{lim}f\left(x\right)=f\left(2\right)=k$
$\Rightarrow k=\underset{x\to 2}{lim}\frac{x^3+x^2-16x+20}{(x-2{)}^2}$
$=\underset{x\to 2}{lim}\frac{(x^2-4x+4)(x+5)}{(x-2)2}=7.$