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Last updated at April 16, 2024 by Teachoo

Ex 5.1, 4 Prove that the function f (x) = π₯^π is continuous at x = n, where n is a positive integer.π(π₯) is continuous at x = n if limβ¬(xβπ) π(π₯)= π(π) Since, L.H.S = R.H.S β΄ Function is continuous at x = n (π₯π’π¦)β¬(π±βπ) π(π) = limβ¬(xβπ) π₯^π Putting π₯=π = π^π π(π) = π^π β΄ Thus limβ¬(xβπ) f(x) = f(n) Hence, f(x) = xn is continuous at x = n