- #1
Felafel
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- 0
Homework Statement
Study the continuity of the function defined by:
## \lim n \to \infty \frac{n^x-n^{-x}}{n^x+n^{-x}}##
3. The Attempt at a Solution
I've never seen a limit like this before.
The only thing I have thought of is inserting random values of x to see it the limit exists.
For instance, in this case, for x=0 I'd have ##\frac{\infty^0-\infty^0}{\infty^0+\infty^0}##
which means the function doesn't exist. but every other value of x, it's okay.
Or am i supposed to solve the limit? (btw, how can I solve a limit for n to infinity??)
thank you