If f(x) ={[(x^2-16)/(x-4), if x≠4][k,if x=4]is continuous at x = 4, find k. ​

Question

If \(f(x) = \begin{cases} \frac{x^2-16}{x-4} & \quad \text{if } x ≠{4}\\ k, & \quad \text{if } x={ 4} \end{cases} \) is continuous at x = 4, find k.

Answer 1

Formula : -

(i) A function f(x) is said to be continuous at a point x=a of its domain, if 
\(\lim\limits_{x \to a}f(x)\) = f(a)

\(f(x) = \begin{cases} \frac{x^2-16}{x-4} & \quad \text{if } x ≠{4}\\ k, & \quad \text{if } x={ 4} \end{cases} \)