Hello!

Trying to find these limits (or show they do not exist)

Using the two path method (to show non-existance)

Not sure how to show they exist (unless they go a certain number by an identity?)

Any help appriciated! Thanks!

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- January 27th 2010, 12:06 PMmatt.qmarTwo Variable LimitsHello!

Trying to find these limits (or show they do not exist)

Using the two path method (to show non-existance)

Not sure how to show they exist (unless they go a certain number by an identity?)

Any help appriciated! Thanks!

- January 27th 2010, 05:20 PMAryth
You can say that these limits do not exist in similar ways to single variable limits.

The first one yields an indeterminant form... So it may or may not exist.

To tackle this one is a bit of work but I'll work on it a little bit and edit this later.

For the second one, look below.

The third one is a classic example of multiple paths to prove nonexistence.

If you plug everything in you immediately see a 0 in the denominator, so it is indeterminate. So, we try a random path... Say, y = x... Then we get:

Now, let's try (Just to mix it up)

=

We plug and chug to get:

Which is NOT zero, so it does not exist.

Hope that helps. - January 27th 2010, 05:37 PMpickslides
- January 27th 2010, 05:39 PMAryth
- January 27th 2010, 06:43 PMmatt.qmar
Thanks!!

For the first limit, so far, I have, if we approach from any line y=mx,

as goes to 0, goes to 0. So the limit of

is 1, and the whole thing is,

which is different for each m, so the limit does not exist.

Not sure if this is legitimate? Hope so! Is there another way to do it? - January 27th 2010, 06:51 PMAryth