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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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