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

Solution:

A function is said to be continuous when the graph of the function is a single unbroken curve.

According to the given problem:

The given function is

f(x) = xⁿ

It is observed that f is defined at all positive integers, n,

and its value at n is nⁿ.

Then,

lim_x→n f(n) = lim_x→n (xⁿ)

= xⁿ

⇒ lim_x→n f(x) = f(n)

Therefore, f is continuous at n, where n is a positive integer

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 4

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

Summary:

The function f(x) = xⁿ is continuous at x = n, where n is a positive integer.A function is said to be continuous when the graph of the function is a single unbroken curve