How can I prove this limit is 0. Can I use squeeze theorem or use other method?
$\lim\limits_{(x,y)\to(0,0)}\frac{sin(x^2-y^2)}{\sqrt{|x|+|y|}}=0$
How to find a multivariable limit using trigonometry function?
0
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calculus
multivariable-calculus
1 Answers
2
Hint: write it as $\;\;\lim\limits_{(x,y)\to(0,0)}\cfrac{\sin(x^2-y^2)}{x^2-y^2} \cdot \cfrac{\left(|x|-|y|\right)\,\left(|x|+|y|\right)}{\sqrt{|x|+|y|}}\;$.