what is the difference between a problem where the limit is infinity or negative infinity and a problem where the limit does not exist?

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what is the difference between a problem where the limit is infinity or negative infinity and a problem where the limit does not exist?

Mathematics
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A problem in which the limit does not exist literally does not have any value. Whereas a limit that is infinity does have a value - it's just infinity. For example, \[\lim_{x \rightarrow \infty}x^2\] \lim_{x \rightarrow \infty}cos(x) \] In the first case the limit is \( \infty \) because the function obviously keeps getting larger and larger as you let x go to \( \infty \). In the second case the limit does not exist because as you let x go to \( \infty \) the function does not approach any value (or \( \infty \) ). Remember that in order for a limit to exist the function must be approaching a value as you let x appoach whatever value you are using ( \( \infyt \) ) in this case...
Arg, couldn't type in my math... The second limit should be, \[\lim_{x \rightarrow \infty}cos(x) \]

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