Question

What is the value of \(\lim\limits_{y \rightarrow \pi/2}\frac{sin⁡ x}{x}\)?

(a) \(\frac{2}{\pi}\)

(b) \(\frac{\pi}{2}\)

(c) 1

(d) 0

The question was posed to me in an internship interview.

Enquiry is from Limits of Trigonometric Functions topic in portion Limits and Derivatives of Mathematics – Class 11

Answer 1

The correct option is (a) \(\frac{2}{\pi}\)

To explain I would say: sin ⁡\(\frac{\pi}{2}\) = 1

\(\lim\limits_{y \rightarrow \pi/2}\frac{sin⁡x}{x} = \frac{sin⁡\frac{π}{2}}{\frac{\pi}{2}}\)

= \(\frac{1}{\frac{\pi}{2}}\)

= \(\frac{2}{\pi}\)