Match the conditions/expressions in Column I with statement in Column II. (A) sin (pi[x])

Question

Match the conditions/expressions in Column I with statement in Column II.

Column I	Column II
(A) sin (pi[x])	(p) differentiable everywhere
(B) sin {pi(x - [x])}	(q) nowhere differentiable
	(r) not differentiable at 1 and -1

 

Answer 1

A → p; B → r

Explanation:

We know [x] ∈ I, ∀ x ∈ R. Therefore,

sin(pi[x]) = 0, ∀ x ∈ R. By theory we know that sin (pi[x]) is differentiable everywhere, therefore (A) ↔ (p).

Again, f(x) = sin{pi(x - [x])}

Now, x - [x] = {x} then pi(x - [x]) = pi{x}

Which is not differentiable at x ∈ I.

Therefore, (B) ↔ (r ) is the answer.