Question

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Let \(f\) be a function defined by \[ f(x) = \begin{cases} \dfrac{\tan x}{x}, & x \neq 0 1, & x = 0 \end{cases} \] Assertion (A): \(x = 0\) is point of minima of \(f\).
Reason (R): \(f'(0) = 0\). In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Use series expansion near \(x=0\) to easily determine behavior of functions involving trigonometric limits.

Answer 1

The Correct Option is A