Check sibling questions

If f (x) = x 2 sin 1/x, where x ≠ 0, then the value of the function f at x = 0, so that the function is continuous at x = 0 , is

(A) 0  

(B) – 1

(C) 1 

(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 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) – 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 = 𝑓(0) if lim┬(xβ†’0^βˆ’ ) 𝑓(π‘₯)=lim┬(xβ†’0^+ ) " " 𝑓(π‘₯)= 𝑓(0) LHL at x β†’ 0 lim┬(xβ†’0^βˆ’ ) f(x) = lim┬(hβ†’0) f(0 βˆ’ h) = lim┬(hβ†’0) f(βˆ’h) = lim┬(hβ†’0) (βˆ’β„Ž)^2 π’”π’Šπ’β‘γ€–πŸ/((βˆ’π’‰))γ€— = lim┬(hβ†’0) β„Ž^2 π’Œ = 02 .π‘˜ = 0 RHL at x β†’ 0 lim┬(xβ†’0^+ ) f(x) = lim┬(hβ†’0) f(0 + h) = lim┬(hβ†’0) f(h) = lim┬(hβ†’0) β„Ž^2 π’”π’Šπ’β‘γ€–πŸ/𝒉〗 = lim┬(hβ†’0) β„Ž^2 π’Œ = 02. π‘˜ = 0 Since, L.H.L = R.H.L = 𝑓(0) 0=𝑓(0) ∴ f (0) =𝟎 So, the correct answer is (A)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.