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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

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### Transcript

Question 7 The value of k which makes the function defined by f (x) = {β 8(π ππ 1/π₯," if " π₯β "0 " @π ", if x " ="0" )β€ , continuous at x = 0 is 8 (B) 1 (C) β1 (D) None of these At π = 0 f(x) is continuous at π₯ =0 if L.H.L = R.H.L = π(0) if 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) sinβ‘(1/(ββ)) = (πππ)β¬(π‘βπ) γβπππγβ‘(π/π) = (πππ)β¬(ββ0) (βm) = β m RHL at x β 0 limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h) = limβ¬(hβ0) f(h) = (πππ)β¬(π‘βπ) πππβ‘(π/π) = (πππ)β¬(ββ0) (m) = m β΄ L.H.L and R.H.L can never be equal as one is always negative of another. Hence, there does not exist any value of k for which f(x) is continuous at π₯=0 So, the correct answer is (D)