Question

What is the value of the limit f(x) = \(\frac{x^2+\sqrt {2x}}{x^2-4x}\) if x approaches infinity?

(a) 0

(b) 2

(c) 1/2

(d) 4

I got this question during an online interview.

My enquiry is from Limits in portion Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct choice is (a) 0

To explain I would say: This is of the form \(\frac{\infty}{\infty}\), therefore we use L’Hospital’s rule and differentiate the numerator and denominator.

= \(\lim\limits_{x \rightarrow \infty}\frac{2x+\sqrt{2/x}}{2x–4}\)

= \(\lim\limits_{x \rightarrow \infty}⁡\)√2 x^-3/2

= 0