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

Transcript

Ex 5.1, 4 Prove that the function f (x) = π‘₯^𝑛 is continuous at x = n, where n is a positive integer. Let 𝑓(π‘₯) = π‘₯^𝑛 We need to prove that 𝑓(π‘₯) = π‘₯^𝑛 is continuous at x = n 𝑓 is continuous at x = n if lim┬(x→𝑛) 𝑓(π‘₯)= 𝑓(𝑛) lim┬(x→𝑛) 𝑓(π‘₯) = lim┬(x→𝑛) π‘₯^𝑛 Putting π‘₯=𝑛 = 𝑛^𝑛 𝑓(π‘₯) = π‘₯^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
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.