Determine the value of k for which the function $f(x)=\left\{\begin{array}{cc}\frac{x^2-9}{x-3} & , x \neq 3 \\ k & , x=3\end{array}\right.$ is continuous at x = 3
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
$f(3)=k$
$\underset{x→3}{\lim}\frac{x^2-9}{x-3}=\underset{x→3}{\lim}x+3=6$
so (k = 3) as f is continuous at $x=3$