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Question
Let f(x) = |sin x|. Then ______.
Options
f is everywhere differentiable
f is everywhere continuous but not differentiable at x = nπ, n ∈ Z
f is everywhere continuous but not differentiable at x = `(2"n" + 1) pi/2`, n ∈ Z
None of these
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Solution
Let f(x) = |sin x|. Then f is everywhere continuous but not differentiable at x = nπ, n ∈ Z.
Explanation:
Given that: f(x) = |sin x|
Let g(x) = sin x and t(x) = |x|
∴ f(x) = tog(x) = t[g(x)] = t(sin x) = |sin x|
Where g(x) and t(x) both are continuous.
∴ f(x) = got(x) is continuous but t(x) is not differentiable at x = 0.
So, f(x) is not continuous at sin x = 0
⇒ x = nπ, n ∈ Z.
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