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Question: If f(x) = \(\lim_{x \rightarrow 0}\frac{\sin\left( \pi\cos^{2}x \right)}{x^{2}}\); x ≠ 0 is continuo...

If f(x) = lim⁡x→0sin⁡(πcos⁡2x)x2\lim_{x \rightarrow 0}\frac{\sin\left( \pi\cos^{2}x \right)}{x^{2}}; x ≠ 0 is continuous at x = 0 then f(0) equals –

A

0

B

1

C

2

D

3

Answer

3

Explanation

Solution

f(0) = Lim⁡x→02x+tan⁡xx=Lim⁡x→0(2+tan⁡xx)\operatorname { Lim } _ { x \rightarrow 0 } \frac { 2 x + \tan x } { x } = \operatorname { Lim } _ { x \rightarrow 0 } \left( 2 + \frac { \tan x } { x } \right)

= 2 + 1= 3