Question

Check the continuity of the function f(x) at x = 0 :
x x , x ≠ 0 f(x) = 0 , x = 0

Answer 1

Answer:

F(x) is continuous at x = 0

Step-by-step explanation:

we are given that

F(x) = 0

Which is the constant polynomial function so its is always be continuous at every where

In our case We have to check continuity at x = 0

Since

F(x) = 0    for all x so when x is zero it must be zero that is

F(0) = 0

And

See

Left hand limit of F(x) at x equal to zero = 0

Right hand limit of F(x) at x equal to zero = 0

So

F(0) = Left hand limit = Right hand limit

Thus

F(x) is continuous at x = 0