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,
(iv) f4(x) = {(x2sin(1/x) if x ≠ 0), (1, if x = 0)
LIST–I |
LIST–II |
P. The function f 4 is |
1. NOT continuous at x = 0 |
Q. The function f 2 is |
2. continuous at x = 0 and NOT differentiable at x = 0 |
R. The function f 3 is |
3. differentiable at x = 0 and its derivative is NOT continuous at x = 0 |
S. The function f 4 is |
4. differentiable at x = 0 and its derivative is continuous at x = 0 |
The correct option is:
(A) P→2; Q→3; R→1; S→4
(B) P→4; Q→1; R→2; S→3
(C) P→4; Q→2; R→1; S→3
(D) P→2; Q→1; R→4; S→3