Question

Let f(x) = [(tanx + sinx )²]. Then

(a) x 0 lim f(x) for x → [0] does not exist

(b) f(x) is not continuous at x = 0

(c) f(x) is not differentiable at x = 0

(d) f'(0) = 0

Answer 1

Correct option (d)

Explanation:

f(x) (tan x +  sinx)²

∵ tan x & sin x are both continuous & differentiable at x = 0 

⇒ f(x) is cont. & diff at x = 0 

f'(x) = 2(tan x + sin x)[sec²x + cosx], f'(0) = 0