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Question

Prove that the function f(x)=xn is continuous at x=n, where n is a positive integer.


Solution

Here, f(x)=xn

          limxn f(x)=limxn x^n = n^n

and                       f(n)=nn                                   [f(×)=×n]

            limxn f(x) =  f(n)

                                Thus, f(x) is continuous at x=n, where n is a positive integer.

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