Question

Let f₁ : R →R, f₂ :(-π/2,π/2)→R, f₃ : (-1, e^π/2-2)→R and f₄ : R → R be functions defined by

(i) f₁(x)=sin(√1-e-^{x^2}),

(ii) f2(x)={|sinx|/tan^-1x  if x≠0,     1 if x=0, where the inverse trigonometric function tan^-1x assumes values in(-π/2,π/2)

(iii) f₃(x) = [sin(loge(x + 2))], where, for t ∈ R, [t] denotes the greatest integer less than or equal to t,

The correct option is :

Answer 1

Answer:D

Solution:

f₃' (x) is 0 in neighbourhood of x = 0 so f₃' (x) is continuous at x = 0
(iv) f₄(x) is continuous at x = 0
f₄'(x) is also differentiable at x = 0​