anonymous
  • anonymous
How do I use the squeeze/Sandwich theorem for Multivariable limits?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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zzr0ck3r
  • zzr0ck3r
example?
abb0t
  • abb0t
Same as you did for single variable limits.
anonymous
  • anonymous
\[\lim_{(x,y) \rightarrow (0,0)}\frac{ xy }{\sqrt{x^2+y^2} }\]

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anonymous
  • anonymous
The lit is indeed 0 but how do I show that using the squeeze theorem?
anonymous
  • anonymous
limit**
anonymous
  • anonymous
Lol, Multivarible isn't really THAT hard. It is hard.
anonymous
  • anonymous
Like what do functions do I take the limit between. How would I know that?
anonymous
  • anonymous
two***
Jhannybean
  • Jhannybean
oh you mean your f(x) and your g(x)....
anonymous
  • anonymous
Yeah. I know how to do it for single variable but not Multivariable.
zzr0ck3r
  • zzr0ck3r
same way I guess, find one you know is for sure smaller and for sure bigger where there limits are equal:)
anonymous
  • anonymous
How would I know? :P . There are an infinite number of possibilities.
zzr0ck3r
  • zzr0ck3r
same way you know for single variable I guess...
zzr0ck3r
  • zzr0ck3r
im trying to come up with one...
zzr0ck3r
  • zzr0ck3r
are you sure this has finite limit?
anonymous
  • anonymous
yep.
anonymous
  • anonymous
According to the textbook this approaches 0.
anonymous
  • anonymous
Which is true because no matter what curve I choose for a path the limit goes to 0.
zzr0ck3r
  • zzr0ck3r
hmm have you tried many paths?
zzr0ck3r
  • zzr0ck3r
o I C
anonymous
  • anonymous
How do I exactly pick the two functions? Is there any specific way?
zzr0ck3r
  • zzr0ck3r
assume xy >=0 0=< xy/ √x² + y² <= (x² + y²) / 2√x² + y² -->0
zzr0ck3r
  • zzr0ck3r
do the same thing for xy<0
anonymous
  • anonymous
Okay. So it just depends on the function I guess?
zzr0ck3r
  • zzr0ck3r
yes for sure
anonymous
  • anonymous
Thanks :) .
zzr0ck3r
  • zzr0ck3r
np

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