Question

What is the value of \(\lim\limits_{x \rightarrow 3}\frac{x^2-9}{x–3}\)?

(a) 0

(b) 3

(c) Infinity

(d) 6

This question was posed to me in a job interview.

Question is from Limits in chapter Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct choice is (d) 6

For explanation I would say: When x tends to 3, both the numerator and the denominator become 0 and it becomes of the form, \(\frac{0}{0}\).

Therefore, we use L’Hospital’s rule, which states the we differentiate the numerator and the denominator, until a definite answer is reached.

On differentiating once we get,

\(\lim\limits_{x \rightarrow 3}\frac{2x}{1}\)

Since, this not an indeterminate form now, we can substitute the value of x.

= 2 x 3

= 6