Limits, Continuity and Differentiability
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Question : 22
Total: 51
Let f 1 : ℝ → ℝ , f 2 : ( −
,
) → ℝ , f 3 ( − 1 , e
− 2 ) → ℝ f 4 : ℝ → ℝ
(i)f 1 ( x ) = s i n ( √ 1 − e − x 2 )
(ii)f 2 ( x ) = {
where the inverse trigonometric functiont a n − 1 x ( −
,
)
(iii)f 3 ( x ) = [ s i n ( log e ( x + 2 ) ) ] , t ∊ ℝ , [ t ]
(iv)f 4 ( x ) = {
The correct options is:
(i)
(ii)
where the inverse trigonometric function
(iii)
(iv)
| List - I | List - II |
|---|---|
| P. the function | 1. NOT continuous at |
| Q. The function | 2. Continuous at |
| R. The function | 3. Differentiable at |
| S. The function | 4. Differentiable at |
| P | Q | R | S | |
|---|---|---|---|---|
| A) | 2 | 3 | 1 | 4 |
| B) | 4 | 1 | 2 | 3 |
| C) | 4 | 2 | 1 | 3 |
| D) | 2 | 1 | 4 | 3 |
[JEE Adv 2018 P2]
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