Question

Which of the following limits does not yield 1?

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

(b) \(\lim\limits_{x \rightarrow 0}\frac{⁡tan x}{cot x}\)

(c) \(\lim\limits_{x \rightarrow 0}(\frac{1}{e^x}+cos⁡ x)\)

(d) \(\lim\limits_{x \rightarrow 0}\) x cosec x

This question was posed to me in an internship interview.

Question is taken from Limits of Trigonometric Functions in chapter Limits and Derivatives of Mathematics – Class 11

Answer 1

Right choice is (c) \(\lim\limits_{x \rightarrow 0}(\frac{1}{e^x}+cos⁡ x)\)

The best explanation: \(\lim\limits_{x \rightarrow 0}(\frac{1}{e^x} + sin⁡ x) = \frac{1}{e^0}\) + cos (0)

= 1 + 1

= 2