Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

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

Can you answer this question?

1 Answer

0 votes
  • If $f$ is a real function on a subset of the real numbers and $c$ a point in the domain of $f$, then $f$ is continous at $c$ if $\lim\limits_{x\to c} f(x) = f(c)$.
Given $f(x) = x^n$:
$\Rightarrow \lim\limits_{x\to n} f(x) = \lim\limits_{x\to n} f(x) = x^n = n^n$
$\Rightarrow f(n) = n^n$
Therefore, $f$ is continuous at $x=n$
answered Apr 4, 2013 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App