Answer
$1$
Work Step by Step
Solve the limit $\lim\limits_{(x,y) \to (0,0)} \cos [\dfrac{x^2+y^2}{x+y+1}]$
$\lim\limits_{(x,y) \to (0,0)} \cos [\dfrac{x^2+y^2}{x+y+1}]=\cos [\dfrac{0^2+0^2}{0+0+1}]$
or, $\cos (0)=1$
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