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in Limit, continuity and differentiability by (54.8k points)

Let S = {t ∈ R : f(x) = |x - π|.(e|x| - )sin|x| is not differentiable at t }. Then, the set S is equal to

(A) {0} 

(B) {π

(C) {0, π

(D) ϕ(an empty set)

1 Answer

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Answer is (D) ϕ(an empty set)

Given:

f(x) = |x - π|. (e|x| - )sin|x|

According to the given options, we have to check only at x = 0 and at x = π.

Therefore, it is differentiable at x = 0.

Therefore, it is differentiable at x = π. Hence, the set S is equal to ϕ(an empty set).

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