Question

Let f1 : R →R, f2 :(-π/2,π/2)→R, f3 : (-1, eπ/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 = 0u200b