Question

If limit of `f(x)=27` as `x->c`, what the limit of `root3(f(x))` as `x->c`?

Answer 1

Use the rule `lim_(xrarra)f(x)^b=(lim_(xrarra)f(x))^b`. So:

`lim_(xrarrc)root3(f(x))=lim_(xrarrc)(f(x))^(1/3)=(lim_(xrarrc)f(x))^(1/3)`

Since `lim_(xrarrc)f(x)=27`:

`=(27)^(1/3)=(3^3)^(1/3)=3`