A few limit questions.


by AndreTheGiant
Tags: limit
AndreTheGiant
AndreTheGiant is offline
#1
Oct10-11, 03:39 PM
P: 28
1. The problem statement, all variables and given/known data
Hello. I have a few questions I wanted to run by just to make sure I did them right.

all the below have lim (x,y) -> (0,0)

1)

2)



2. Relevant equations



3. The attempt at a solution

ok so this is what i did for the following.

1) if i approach from the x axis and y axis, both the limits give me -3/0 as an answer. If i approach from y = ax, i also get -3/0 as the final answer. So the limit does not exist? What other methods can i use here because I'm not sure if this is right.

2) approaching from the y-axis I get lim y-> 0 of y^2/y^2 = 1
approaching from the x-axis i get lim x-> 0 3x^2/x^2 = 3
since those two aren't equal I can conclude that the limit does not exist.
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SammyS
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#2
Oct10-11, 04:03 PM
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Andre,

Welcome to PF.

You will get better response if you post only one or two problems per thread. (That's also in the Forum Rules.)

For (1):

You might still want to see if the limit is +∞ or if it's -∞ -- or just plain DOES NOT EXIST. Check that along the y-axis from the positive versus the negative direction.

For (2):

That's correct.

For (3):

Also correct.
AndreTheGiant
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#3
Oct10-11, 04:06 PM
P: 28
Thanks for the reply. I edited my post to have 2 questions only. Thanks!

SammyS
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#4
Oct10-11, 04:08 PM
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A few limit questions.


Post the other two in another thread


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