CONTINUITY AND DIFFERENTIABILITY — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsCONTINUITY AND DIFFERENTIABILITY5 Marks
Question
Prove that the function $f(x) = x^n$ is continuous at $x = n$, where $n$ is a positive integer.
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Answer
Here $f(x) = x^n$, 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 $f(n) = n^n$
$\therefore\ ^{\ \ \text{Lt}}_{\text{x}\rightarrow\text{n}}\text{f(x)} = \text{f(n)}$
$\therefore$ f is continous at x = n.
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