1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
  3. Ex 5.1
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Ex 5.1 ,5 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 16, 2024 by Teachoo

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Ex 5.1, 5 Is the function f defined by 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ continuous at 𝑥 = 0 ? At 𝑥 = 1 ? At 𝑥 = 2 ? Given 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ At x = 0 For x = 0, f(x) = x Since this a polynomial It is continuous ∴ f(x) is continuous for x = 0 At x = 1 f(x) is continuous at 𝑥 =1 if L.H.L = R.H.L = 𝑓(1) if lim┬(x→1^− ) 𝑓(𝑥)=lim┬(x→1^+ ) " " 𝑓(𝑥)= 𝑓(1) 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ Since there are two different functions on the left & right of 1, we take LHL & RHL . LHL at x → 1 lim┬(x→1^− ) f(x) = lim┬(h→0) f(1 − h) = lim┬(h→0) (1−ℎ) = 1 − 0 = 1 RHL at x → 1 lim┬(x→1^+ ) f(x) = lim┬(h→0) f(1 + h) = lim┬(h→0) 5 = 5 Since L.H.L ≠ R.H.L f(x) is not continuous at x = 1 At x = 2 For x = 2, f(x) = 5 Since this a constant function It is continuous ∴ f(x) is continuous for x = 2
  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise

    3. Ex 5.1

    Ex 5.2 →
Ex 5.2 →
Chapter 5 Class 12 Continuity and Differentiability
Serial order wise

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Davneet Singh

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