Question

What is the value of \(\lim\limits_{x \rightarrow 4} \frac{x^2-2x-8}{x-4}\)?

(a) 0

(b) 2

(c) 8

(d) 6

I had been asked this question during an interview for a job.

My question comes from Limits in section Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct answer is (d) 6

To explain I would say: The denominator becomes 0, as x approaches 4.

\(\lim\limits_{x \rightarrow 4} \frac{x^2-2x-8}{x-4}\) Here, if we factorize the numerator we get:

\(\lim\limits_{x \rightarrow 4} \frac{(x – 4)(x + 2)}{x – 4}\)

We can now cancel out (x – 4) from both the numerator and denominator.

We get, \(\lim\limits_{x \rightarrow 4}\)(x + 2) = 6