Thread: Difficult Limit

Limit as x goes towards 0 for the function (e^x-1)^2/(sin(e^x-1))

Any help would be much appreciated

Originally Posted by DylanRenke

Limit as x goes towards 0 for the function (e^x-1)^2/(sin(e^x-1))

Any help would be much appreciated

To simplify things let



If we take the limit as this is the same as the limit as

Now this gives you the limit



This gives

Why doesnt that last line just give you 0/0? because when u approaches 0, it equals 0, and when sin(u) approaches 0, its zero as well?

Originally Posted by DylanRenke

Why doesnt that last line just give you 0/0? because when u approaches 0, it equals 0, and when sin(u) approaches 0, its zero as well?

This is a well known limit and its value should be known. The proof is a bit lengthy and requires a bit of trigonometry and the use of the squeeze theorem.

Do you need a proof?

It would be quiet helpful, because i really do not understand it.

Actually, i have found that the professor told us to memorize that limit. Thank you for the help