Prove that the function f(x) = xn is continuous at x = n, where n… - Vidyadip

Question

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

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Answer

Here f(x) = xⁿ, Where is a possitive integer.
$^{\ \ \text{Lt}}_{\text{x}\rightarrow\text{n}}\text{f(x)} = ^{\ \ \text{Lt}}_{\text{x}\rightarrow\text{n}}(\text{x}^\text{n}) = \text{n}^\text{n}$
Now f is defined at x = n
and f(n) = nⁿ
$\therefore\ ^{\ \ \text{Lt}}_{\text{x}\rightarrow\text{n}}\text{f(x)} = \text{f(n)}$
$\therefore$ f is continous at x = n.

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