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You play as a man named Arty who left his home for what he believes is a peaceful protest. Unfortunately, the world has turned violent and Arty is now a wanted man. Arty flees, searching for a way to hide from the police, but he soon discovers a conspiracy that threatens the world of Filament. You must take on the role of this lone man and determine how this world functions. And you must figure out the secrets of Filament before they figure you out.
SYSTEM REQUIREMENTS:
OS: Windows Vista/XP/2000/NT4
Processor: Intel Core2 Duo 2GHz
Memory: 2GB RAM
Graphics: DirectX 9.0 compatible
DirectX: Version 9.0
Input: Keyboard
Storage: 700 MB available spaceQ:

I can’t use the derivative of a transcendental function to find the limit of a function.

Hey guys this is my first question so I apologize if it’s sort of stupid or if I’m missing some basic knowledge but I don’t know how to solve this problem.
Lets say I have the function:
$$
f(x) = \frac{\sqrt[3]{x^{2}+5}-3x+5}{\sqrt[3]{x^{2}+5}+3x-2}
$$
and I want to find the limit of f(x) when x goes to infinity with $x>0$
the answer is $0$ but I think that $f(x)$ goes to infinity, since $\sqrt[3]{x^{2}+5}$ goes to infinity.
could someone help me out with this?

A:

You are correct that $\sqrt[3]{x^2 + 5} \to \infty$ for $x \to \infty$, but the function is not defined for $xHide Caption

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