Question

How do I use the squeeze/Sandwich theorem for Multivariable limits?

Answer 1

example?

Answer 2

Same as you did for single variable limits.

Answer 3

\[\lim_{(x,y) \rightarrow (0,0)}\frac{ xy }{\sqrt{x^2+y^2} }\]

Answer 4

The lit is indeed 0 but how do I show that using the squeeze theorem?

Answer 5

limit**

Answer 6

Lol, Multivarible isn't really THAT hard. It is hard.

Answer 7

Like what do functions do I take the limit between. How would I know that?

Answer 8

two***

Answer 9

oh you mean your f(x) and your g(x)....

Answer 10

Yeah. I know how to do it for single variable but not Multivariable.

Answer 11

same way I guess, find one you know is for sure smaller and for sure bigger where there limits are equal:)

Answer 12

How would I know? :P . There are an infinite number of possibilities.

Answer 13

same way you know for single variable I guess...

Answer 14

im trying to come up with one...

Answer 15

are you sure this has finite limit?

Answer 16

yep.

Answer 17

According to the textbook this approaches 0.

Answer 18

Which is true because no matter what curve I choose for a path the limit goes to 0.

Answer 19

hmm have you tried many paths?

Answer 20

o I C

Answer 21

How do I exactly pick the two functions? Is there any specific way?

Answer 22

assume xy >=0
0=< xy/ √x² + y² <= (x² + y²) / 2√x² + y² -->0

Answer 23

do the same thing for xy<0

Answer 24

Okay. So it just depends on the function I guess?

Answer 25

yes for sure

Answer 26

Thanks :) .

Answer 27

np