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## Homework Statement

Why is it?

lim{x-> infinity} f(x)/x = infinity => lim{x-> infinity} f(x) = infinity

What is evidence?

Thank you very much.

- Thread starter gymko
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- #1

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Why is it?

lim{x-> infinity} f(x)/x = infinity => lim{x-> infinity} f(x) = infinity

What is evidence?

Thank you very much.

- #2

Mark44

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As for evidence, if you assume that lim f(x) is finite or doesn't exist, then lim [f(x)/x] is 0 or doesn't exist as x gets large, which is a contradiction. If you were going to prove this, you would have to be a little more careful, but maybe you get the idea I'm trying to convey.

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