Question

Let $f\left(x\right)=\frac{x^3+x^2-16x+20}{{(x-2)}^2}ifx\ne 2,=k,ifx=2.$ If $f\left(x\right)$ is continuous for all x,then $k=b\times 7$ Find b

Answer 1

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