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OS: Windows Vista/XP/2000/NT4
Processor: Intel Core2 Duo 2GHz
Memory: 2GB RAM
Graphics: DirectX 9.0 compatible
DirectX: Version 9.0
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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?


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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