Example 4 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 4 Show that the function f given by π(π₯)={β(π₯3+3, ππ π₯β 0@1, ππ π₯=0)β€ is not continuous at x = 0. f(x) is continuous at π₯ =0 if L.H.L = R.H.L = π(0) If (πππ)β¬(π₯β0^β ) π(π₯)=(πππ)β¬(π₯β0^+ ) " " π(π₯)= π(0) Finding LHL and RHL LHL at x β 0 limβ¬(xβ0^β ) f(x) = limβ¬(hβ0) f(0 β h) = limβ¬(hβ0) f(βh) = limβ¬(hβ0) (βh)3 + 3 = 03 + 3 = 3 RHL at x β 0 limβ¬(xβ0^+ ) f(x) = limβ¬(hβ0) f(0 + h) = limβ¬(hβ0) f(h) = limβ¬(hβ0) h3 + 3 = 03 + 3 = 3 But, f(0) = 1 So, LHL = RHL β f(0) Hence, f is not continuous at π = π
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo