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
Answers
Answered by
9
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
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
Similar questions