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

Question

anonymous · Answer

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...

anonymous · Answer

Arg, couldn't type in my math...  The second limit should be,

$$\lim_{x \rightarrow \infty}cos(x) $$