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


  1. Chapter 5 Class 12 Continuity and Differentiability
  2. Serial order wise
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Ex 5.1, 4 Prove that the function f (x) = ﷐𝑥﷮𝑛﷯ is continuous at x = n, where n is a positive integer. Let 𝑓﷐𝑥﷯ = ﷐𝑥﷮𝑛﷯ We need to prove that 𝑓﷐𝑥﷯ = ﷐𝑥﷮𝑛﷯ is continuous at x = 4 𝑓 is continuous at x = n if ﷐lim﷮x→𝑛﷯ 𝑓﷐𝑥﷯= 𝑓﷐𝑛﷯ ∴ Thus ﷐lim﷮x→𝑛﷯ f(x) = f(n) Hence, f(x) = xn is continuous at x = n

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