NCERT Exemplar - MCQs

Chapter 5 Class 12 Continuity and Differentiability
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## (D) none of these

This question is similar to Ex 5.1, 24 - Chapter 5 Class 12 - Continuity and Differentiability

### Transcript

Question 16 If f (x) = x2 sin 1/π₯, where x β  0, then the value of the function f at x = 0, so that the function is continuous at x = 0, is (A) 0 (B) β 1 (C) 1 (D) none of these Given f (x) = x2 sin 1/π₯, when x β  0 To find f (0) f(x) is continuous at π₯=0 if L.H.L = R.H.L = π(0) if limβ¬(xβ0^β ) π(π₯)=limβ¬(xβ0^+ ) " " π(π₯)= π(0) LHL at x β 0 limβ¬(xβ0^β ) f(x) = limβ¬(hβ0) f(0 β h) = limβ¬(hβ0) f(βh) = limβ¬(hβ0) (ββ)^2 πππβ‘γπ/((βπ))γ = limβ¬(hβ0) β^2 π = 02 .π = 0 RHL at x β 0 limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h) = limβ¬(hβ0) f(h) = limβ¬(hβ0) β^2 πππβ‘γπ/πγ = limβ¬(hβ0) β^2 π = 02. π = 0 Since, L.H.L = R.H.L = π(0) 0=π(0) β΄ f (0) =π So, the correct answer is (A)