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

Ex 5.1 ,3 - Chapter 5 Class 12 Continuity and Differentiability - Part 6
Ex 5.1 ,3 - Chapter 5 Class 12 Continuity and Differentiability - Part 7

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Ex 5.1, 3 Examine the following functions for continuity. (c) f (x) = (π‘₯^(2 )βˆ’ 25 )/(π‘₯ + 5), x β‰  –5 f (x) = (π‘₯^(2 )βˆ’ 25 )/(π‘₯ + 5) Putting x = –5 f (βˆ’5) = (γ€–(βˆ’5)γ€—^(2 )βˆ’ 25 )/(βˆ’5 + 5) = (25βˆ’ 25 )/(βˆ’5 + 5) = 0/0 = Undefined Hence, f(x) is not defined at x = βˆ’5 So, we check for continuity at all points except βˆ’5 Let c be any real number except βˆ’5. f is continuous at π‘₯ = 𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) LHS (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(x→𝑐) (π‘₯^2βˆ’ 25)/(π‘₯ + 5) = lim┬(x→𝑐) ((π‘₯ βˆ’ 5) (π‘₯ + 5))/(π‘₯ + 5) = lim┬(x→𝑐) π‘₯βˆ’5 Putting x = c = c βˆ’ 5 RHS f (c) = (𝑐^(2 )βˆ’ 25 )/(𝑐 + 5) = ((𝑐 βˆ’ 5)(𝑐 + 5))/((𝑐 + 5)) = c βˆ’ 5 Let c be any real number except βˆ’5. f is continuous at π‘₯ = 𝑐 if (π₯𝐒𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (except βˆ’5) Thus, we can write that f is continuous for all real numbers except βˆ’5 ∴ f is continuous at each 𝐱 ∈ R βˆ’ {βˆ’πŸ“}

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.