$f(x)=\frac{\sin π[π-x]}{3+[x]}$ i

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

$f(x)=\frac{\sin π[π-x]}{3+[x]}$ is, (where [·] represents greatest integer function)

Options:

differentiable for all x ∈ R

continuous and differentiable for all x ∈ R

continuous and differentiable everywhere except for x ∈ [–3, –2)

f(x) is twice differentiable for all x ∈ R

Correct Answer:

continuous and differentiable everywhere except for x ∈ [–3, –2)

Explanation:

$f(x)=\left\{\begin{matrix}0&;&x ∈ R-[–3, –2)\\N.D.&;&x ∈ [–3, –2)\end{matrix}\right.$

∴ f (x) is continuous and differentiable for all x ∈ R ~ [– 3, – 2).