Question

Why is `f(x)=sqrtx` continuous?

Answer 1

For every number `a` in `(0,oo)`, we have `lim_(xrarra)sqrtx = sqrta`. That is the definition of continuous at `a`.

At `0`, we have `lim_(xrarr0^+) sqrtx = sqrt0` which is the definition of continuous from the right at `0`.

So `sqrtx` is continuous on `[0, oo)`.

`lim_(xrarra)sqrtx = sqrta` can be proven using the definition of limit.