Question

Let $f\left(x\right)=21\frac{x^3+x^2-16x+20}{{(x-2)}^2}$ if $x\ne 2$ value of f(2) so that is a continuous function.

Answer 1

$f\left(2\right)=\underset{x\to 2}{lim}21.\frac{x^3+x^2-16x+20}{(x-2{)}^2}$
$\Rightarrow f\left(2\right)=21.\underset{x\to 2}{lim}\frac{(x-2{)}^2(x+5)}{(x-2{)}^2}=21.\underset{x\to 2}{lim}(x+5)$
$\Rightarrow f\left(2\right)=21\left(7\right)=147$