Limit of a function raised to a fractional power

[mcastillo356]

TL;DR Summary

T'm in front of a statement about limits of a power, and the conditions are not comprehensive by me

Hi, PF
This is the quote:
"If $m$ is an integer and $n$ is a positive integer, then
6. Limit of a power:
$\displaystyle\lim_{x \to{a}}{\left[f(x)\right]^{m/n}}$ whenever $L>0$ if $n$ is even, and $L\neq{0}$ if $m<0$"
What do I understand?
-whenever $L>0$ if $n$ is even: $m$ could be a negative integer, so I could write $L^{-m/n}=\dfrac{1}{L^{m/n}}$. Right?
-and $L\neq{0}$ if $m<0$: so I could write: $-L^{-m/n}=-\dfrac{1}{L^{m/n}}$
I'm I right?I'm not native, excuse the language mistakes

 

[Mark44]

Summary:: T'm in front of a statement about limits of a power, and the conditions are not comprehensive by me

Hi, PF
This is the quote:
"If $m$ is an integer and $n$ is a positive integer, then
6. Limit of a power:
$\lim_{x \to{a}}\left[f(x)\right]^{m/n}$ whenever L>0 if n is even, and $L\neq{0}$ if m<0"

Is the above the complete quote? Is L the limit? It looks like you have omitted something in what you wrote.

I'm guessing that a more complete statement would be something like this:
If $\lim_{x \to a} f(x) = L$, then $\lim_{x \to a}f(x)^{m/n} = L^{m/n}$ whenever $L>0$ if n is even, and $L\neq{0}$ if m<0

What do I understand?
-whenever $L>0$ if $n$ is even: $m$ could be a negative integer, so I could write $L^{-m/n}=\dfrac{1}{L^{m/n}}$. Right?
-and $L\neq{0}$ if $m<0$: so I could write: $-L^{-m/n}=-\dfrac{1}{L^{m/n}}$
I'm I right?I'm not native, excuse the language mistakes

It's probably simpler to get an understanding of the possible values that $a^{m/n}$ can take when a < 0, and whether n is even or odd. I think this might be what you're confused on, and the whole business of limits and functions is really extraneous to what you're confused about.

 

[mcastillo356]

Is the above the complete quote? Is L the limit? It looks like you have omitted something in what you wrote.

I'm guessing that a more complete statement would be something like this:
If $\lim_{x \to a} f(x) = L$, then $\lim_{x \to a}f(x)^{m/n} = L^{m/n}$ whenever $L>0$ if n is even, and $L\neq{0}$ if m<0

That's it. Thanks!

It's probably simpler to get an understanding of the possible values that $a^{m/n}$ can take when a < 0, and whether n is even or odd. I think this might be what you're confused on, and the whole business of limits and functions is really extraneous to what you're confused about.

I've just started the first chapter, that tries to introduce the concept of limits. It's "Calculus", by Robert A. Adams. I will continue reading. Let's see where does it start talking about the issue of limits.