Prove that `f(x)=x^n`, is continuous at `x = 0`.

Prove that f(x)=|x| is continuous at x=0

Prove that f (x) =|x| is continuous at x =0

Show that f(x)=|x| is continuous at x=0

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

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

Prove that f(x)=sin x is continuous at x=(pi)/(2)

f(x)= {(|x-1|",",x ge 0),(-|x|",",x lt 0):} Prove that f(x) is continuous for x in R- {0} .

Prove that f(x)={(x^(2))/(a)-a,a is continuous at x=a

If f((x + 2y)/3)=(f(x) + 2f(y))/3 AA x, y in R and f(x) is continuous at x = 0. Prove that f(x) is continuous for all x in R.

Prove that the function f(x)= x^(2) is continuous at x=0.