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

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

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best_answer

GIven function is
f (x) = x^n
 the function f (x) = x^n is defined for all positive integer, n
f(n) = n^n\\ \lim_{x\rightarrow n}f(x) = n^n\\ \lim_{x\rightarrow n}f(x) = f(n)
Hence,  the function f (x) = x^n is continuous at x = n, where n is a positive integer

Posted by

Gautam harsolia

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