Question

What is the value of the limit \(\lim\limits_{x \rightarrow 0}\frac{sin^2⁡x}{x^2}\)?

(a) 2

(b) 1

(c) Limit does not exist

(d) 4

The question was asked in an interview for job.

My question is based upon Limits of Trigonometric Functions in portion Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct choice is (b) 1

Best explanation: \(\lim\limits_{x \rightarrow 0}\frac{sin^2⁡x}{x^2}\) =

= (\(\lim\limits_{x \rightarrow 0}\frac{sin ⁡x}{x}\) x \(\lim\limits_{x \rightarrow 0}\frac{sinx}{x}\))

We apply L’Hospital’s rule and differentiate numerator and denominator.

= (\(\lim\limits_{x \rightarrow 0}\frac{cos x}{1}\) x \(\lim\limits_{x \rightarrow 0}\frac{cos x}{1}\))

= 1