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Ex 5.1, 4 - Prove that f(x) = xn is continuous at x = n - Ex 5.1

Ex 5.1 ,4 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Ex 5.1, 4 Prove that the function f (x) = π‘₯^𝑛 is continuous at x = n, where n is a positive integer.𝑓(π‘₯) is continuous at x = n if lim┬(x→𝑛) 𝑓(π‘₯)= 𝑓(𝑛) Since, L.H.S = R.H.S ∴ Function is continuous at x = n (π₯𝐒𝐦)┬(𝐱→𝒏) 𝒇(𝒙) = lim┬(x→𝑛) π‘₯^𝑛 Putting π‘₯=𝑛 = 𝑛^𝑛 𝒇(𝒏) = 𝑛^𝑛 ∴ Thus lim┬(x→𝑛) f(x) = f(n) Hence, f(x) = xn is continuous at x = n

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.