Understanding Limit Questions: Approaches and Solutions | Homework Help

[AndreTheGiant]

Homework Statement

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) [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP188519hd2c481i6c46be00004f512a01afdig9ge?MSPStoreType=image/gif&s=27&w=111&h=40

2) [PLAIN]http://www4d.wolframalpha.com/Calculate/MSP/MSP142419hd2d04f3fccfb70000144ef2c7017g2919?MSPStoreType=image/gif&s=43&w=63&h=43

Homework Equations

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.

 

[SammyS]

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]

Thanks for the reply. I edited my post to have 2 questions only. Thanks!

 

[SammyS]

Post the other two in another thread