Limit of a function of more than one variable

  • Thread starter mathe
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  • #1
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Main Question or Discussion Point

Prove that
[tex]\lim_{x \to\0 ,y\rightarrow 0}(x+y)sin\frac{1}{x}sin\frac{1}{y}=0[/tex]
 

Answers and Replies

  • #2
tiny-tim
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welcome to pf!

hi mathe! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
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hi mathe! welcome to pf! :wink:

show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
Here's what I've tried
\[|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)\]
but it seems to me so simple and too obvious...so I'm not sure about the solution
 
  • #4
tiny-tim
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hi mathe! :smile:

(you forgot to type "tex"! :wink:)
Here's what I've tried
[tex]\[|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)\][/tex]
but it seems to me so simple and too obvious...so I'm not sure about the solution
looks fine to me :smile:
 

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