Questioning the Limit of Sin x/|x| as x Approaches 0

[xargon]

Hello all,

I have a question that got me stumped.

lim Sin x/|x|
x->0

The above limit. Does it exist or not? If yes why, and if no why not.

Any help would be greatly appreciated :-)

Thanks,
Xargon

 

[Hurkyl]

Have you tried anything?

Often a good approach when dealing with absolute values is to break the problem into two parts: one where the inside is positive and one where it is negative.

 

[Chaotic42]

Remember that one of the requirements for a limit to exist is the limit must be the same from both sides.

Since 0/0 is undefined, you'll want to try x plus or minus some very small amount.

For example, try .001 for x to determine the limit from the right. Then try -.001 to determine the limit from the left. See if they match up.