Question

Each entry in Column-I is related to exactly in Column-II. Write the correct letter from Column-II against the entry number in Column-I.

| Column I | Column II |
| (i) | sin(πu2009[x]) | (A) | differentiable everywhere |
| (ii) | sin{πu2009(x – [x])} | (B) | nowhere differentiable |
| | | (C) | not differentiable at 1 and-1 where [,] = G.I.F |

Answer 1

(i) Let f(x) = sin(π[x])

Since [x] provides us integer, so f(x) = 0

It is continuous and differentiable everywhere

(ii) Let f(x) = sin(π(x – [x]))

= sin (π{x})

As we know that, {x} is discontinuous at every integral points, so f(x) is disc at all integers

Thus f(x) is non-differentiable at x = – 1 and 1.