Question

What is the value of \(\lim\limits_{x \rightarrow 0}\frac{x \,tanx}{cot\, x}\)?

(a) 0

(b) 1

(c) 2

(d) \(\frac{1}{2}\)

The question was posed to me in a job interview.

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

Answer 1

The correct option is (a) 0

To elaborate: \(\lim\limits_{x \rightarrow 0}\frac{x tanx}{cot x}\) = \(\lim\limits_{x \rightarrow 0}\frac{x\frac{sin⁡ x}{cos ⁡x}}{\frac{cos⁡ x}{sin⁡ x}}\)

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

= 0