Question

What is the value of \(\lim\limits_{y \rightarrow 0}\)(32 x^2 cosec^2 ⁡4x)?

(a) 1

(b) 4

(c) 2

(d) 3

The question was posed to me in semester exam.

My doubt stems from Limits of Trigonometric Functions in portion Limits and Derivatives of Mathematics – Class 11

Answer 1

Correct choice is (c) 2

For explanation I would say: The limit can be written as, \(\lim\limits_{x \rightarrow 0}\frac{32x^2}{sin^2⁡4x}\)

= 2 x \(\lim\limits_{x \rightarrow 0}\frac{4x}{sin 4x}\) x \(\lim\limits_{x \rightarrow 0}\frac{4x}{sin 4x}\)

= 2 x 1 x 1

= 2