Question

Find the value of the constant $\lambda$ so that the given function is continuous at $x=-1$.
$f\left(x\right)=\{\begin{array}{cc}\frac{x^2-2x-3}{x+1},& x\ne -1\\ \lambda ,& x=-1\end{array}$

Answer 1

$\because f\left(x\right)$ is continuous at $x=-1$

$\lambda =\underset{x\to -1}{lim}\frac{x^2-2x-3}{x+1}=\underset{x\to -1}{lim}\frac{(x-3)(x+1)}{x+1}=\underset{x\to -1}{lim}(x-3)=-4$