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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]

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

- Thread starter mathe
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- #1

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Prove that

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

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

- #2

tiny-tim

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hi mathe! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

- #3

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Here's what I've triedhi mathe! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

\[|(x+y)sin\frac{1}{x}sin\frac{1}{y}|\leq |x+y|\rightarrow 0 (as x,y\rightarrow 0)\]

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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Homework Helper

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(you forgot to type "tex"! )

looks fine to meHere'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

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