Match List-I with List-II
|
List-I |
List-II |
|
(A) $f(x) = x. \sin x$ |
(I) is not continuous at $x = -3$ |
|
(B) $f(x)=\frac{|x|}{x},x≠0$ and $f(x) = 1$ at $x = 0$ |
(II) is continuous everywhere |
|
(C) $f(x) = x-[x]$, $[x]$ denotes greatest integer function |
(III) is not differentiable at $x = 1$ |
|
(D) $f(x) = e^{|x-1|}$ |
(IV) is not continuous at $x = 0$ |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
| List-I | List-II | Explanation |
|---|---|---|
| (A) f(x) = x·sinx | (II) is continuous everywhere | Product of continuous functions (x and sinx) |
| (B) f(x) = |x|/x, x ≠ 0; f(0) = 1 | (IV) is not continuous at x = 0 | Left limit = −1, right limit = 1, f(0) = 1 ⇒ discontinuous |
| (C) f(x) = x − [x] | (I) is not differentiable at x = −3 | f(x) ={x}= fractional part function ⇒ not differentiable at all integers |
| (D) f(x) = e|x−1| | (III) is not differentiable at x = 1 | Non-differentiable at the corner point x = 1 (|x−1|) |