Determine if a limit exists. If the limit approaches infinity or negative infinity, state which one the limit approaches.
The limit of... 2/sin(x) as x approaches 0
Thanks.

Question

Determine if a limit exists. If the limit approaches infinity or negative infinity, state which one the limit approaches.
The limit of...  2/sin(x) as x approaches 0
Thanks.

kropot72 · Answer

Consider values of x close to zero, both when the values are greater than zero (x approaching zero from above) and when the values of x are less than zero (x approaching zero from below). As x approaches zero from below the value of the function tends to negative infinity and as x approaches zero from above the function tends to positive infinity.
Do you think that a limit can exist under the conditions described above?

anonymous · Answer

Can it be both positive and negative infinity?

kropot72 · Answer

No. If the function has a limit, the limit must be the same when approached from above and below.

kropot72 · Answer

@pokemonmaster96 Can you now see what the answer to the question must be?

anonymous · Answer

There is no limit?

kropot72 · Answer

Correct. A limit for the function as x approaches zero does not exist.

anonymous · Answer

Okay, that makes sense. Thank you :)

kropot72 · Answer

You're welcome :)