Ex 5.1 ,3 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

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Ex 5.1 ,3 - Chapter 5 Class 12 Continuity and Differentiability - Part 4

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

Transcript

Ex 5.1, 3 Examine the following functions for continuity. (b) f (x) = 1/(π‘₯ βˆ’ 5) , x β‰  5 f (x) = 1/(π‘₯ βˆ’ 5) At x = 5 f (x) = 1/(5 βˆ’ 5) = 1/0 = ∞ Hence, f(x) is not defined at x = 5 So, we check for continuity at all points except 5 Let c be any real number except 5. f is continuous at π‘₯ = 𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) LHS (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(π‘₯βŸΆπ‘)⁑〖1/(π‘₯ βˆ’ 5)γ€— = 1/(𝑐 βˆ’ 5) RHS 𝒇(𝒄) = 1/(𝑐 βˆ’ 5) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (except 5) Thus, we can write that f is continuous for all real numbers except 5 ∴ f is continuous at each 𝐱 ∈ R βˆ’ {πŸ“}

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.