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  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

Transcript

Example 15 (Introduction) Find all the points of discontinuity of the greatest integer function defined by 𝑓 (π‘₯) = [π‘₯], where [π‘₯] denotes the greatest integer less than or equal to π‘₯ Greatest Integer less than equal to π‘₯ Value of 𝒙 Value of Greatest Integer 3 3 3.1 3 3.9999 3 2.9999 2 Going by Same concept Value of Greatest Integer Example 15 Find all the points of discontinuity of the greatest integer function defined by 𝑓 (π‘₯) = [π‘₯], where [π‘₯] denotes the greatest integer less than or equal to π‘₯ Given f (x) = [π‘₯] Let c be any integer f is continuous at x = c if LHL = RHL = f(c) i.e. lim┬(π‘₯→𝑐^βˆ’ )⁑〖𝑓(π‘₯)γ€— = lim┬(π‘₯→𝑐^+ )⁑〖𝑓(π‘₯)γ€— = f(c) LHS lim┬(π‘₯→𝑐^βˆ’ )⁑〖𝑓(π‘₯)γ€— =lim┬(π‘₯→𝑐^βˆ’ )⁑[π‘₯] = c βˆ’ 1 RHS lim┬(π‘₯→𝑐^+ )⁑〖𝑓(π‘₯)γ€— =lim┬(π‘₯→𝑐^+ )⁑[π‘₯] = c Since lim┬(π‘₯→𝑐^βˆ’ )⁑〖𝑓(π‘₯)γ€— β‰  lim┬(π‘₯→𝑐^+ )⁑〖𝑓(π‘₯)γ€— ∴ f is discontinuous for all integers

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.