# Find the limits: lim_{(x,y)rightarrow(0,0)}cosfrac{x^2+y^3}{x+y+1}

Find the limits:
$\underset{\left(x,y\right)\to \left(0,0\right)}{lim}\mathrm{cos}\frac{{x}^{2}+{y}^{3}}{x+y+1}$
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delilnaT
Given:
$\underset{\left(x,y\right)\to \left(0,0\right)}{lim}\mathrm{cos}\frac{{x}^{2}+{y}^{3}}{x+y+1}$
On plugging in the value (x,y)=(0,0)
$\underset{\left(x,y\right)\to \left(0,0\right)}{lim}\mathrm{cos}\frac{{x}^{2}+{y}^{3}}{x+y+1}=\mathrm{cos}\left(\frac{{0}^{2}+{0}^{3}}{0+0+1}\right)$
On simplifying
$\underset{\left(x,y\right)\to \left(0,0\right)}{lim}\mathrm{cos}\frac{{x}^{2}+{y}^{3}}{x+y+1}=1$
Jeffrey Jordon