Question

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

(a) 1

(b) 2

(c) 0

(d) Limit does not exist

I have been asked this question in an online quiz.

Enquiry is from Limits in division Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct choice is (a) 1

Explanation: Since it is of the form \(\frac{\infty}{\infty}\), we use L’Hospital’s rule and differentiate the numerator and denominator

L = \(\lim\limits_{x \rightarrow \infty}\frac{x^2-9}{x^2–3x+2}\)

On differentiating once, we get \(\lim\limits_{x \rightarrow \infty}\frac{2x}{2x}\)

Which is equal to, \(\lim\limits_{x \rightarrow \infty}\) ⁡1 = 1.