Question

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

Class 12 - Math - Continuity and Differentiability

Answer 1

Refers to the attachment..

Hope helps✌

Answer 2

It is given that 
f(x) = xⁿ { this function is defined for all positive integer n 

this f(n) = nⁿ 

Now lim x→n f(x) = lim x→n xⁿ 
= nⁿ 
thus f(n) = lim x→n f(x) 
hence function is continuous at x = n