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

Last updated at Jan. 3, 2020 by Teachoo

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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 = n 𝑓 is continuous at x = n if lim┬(x→𝑛) 𝑓(𝑥)= 𝑓(𝑛) lim┬(x→𝑛) 𝑓(𝑥) = lim┬(x→𝑛) 𝑥^𝑛 Putting 𝑥=𝑛 = 𝑛^𝑛 𝑓(𝑥) = 𝑥^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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Chapter 5 Class 12 Continuity and Differentiability

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