Match the column:
Column-I | Column-II |
(i) f(x) = sin | x | | [A] Continuous Everywhere |
(ii) f(x) = | [B] Differential everywhere |
(iii) f(x) = | [C] Even |
(iv) f(x) = e–|x| | [D] Periodic |
Text Solution
Verified by Experts(i) [A]; (ii) [A]; (iii) [A]; (iv) [A]
Ans.
(i) [A], [C]
(ii) [A], [B]
(iii) [A], [C], [D]
(iv) [A], [C]
Sol. (i) f(x) = sin | x | = 
Continuous everywhere, not differentiable at x = 0, even
(ii)
f(x) = 
= 
Continuous everywhere and differentiable
(iii)
f(x) = 
⇒ f(x) = 
Continuous everywhere, not differentiable when
sin 
= 0, even and periodic
(iv)
f(x) = e –| x | = 
Continuous everywhere, not differentiable at
x = 0 and even.
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