# Use the method of your choice to evaluate the following limits. lim_{(x,y)rightarrow(2,0)}frac{1-cos y}{xy^2}

Use the method of your choice to evaluate the following limits.
$\underset{\left(x,y\right)\to \left(2,0\right)}{lim}\frac{1-\mathrm{cos}y}{x{y}^{2}}$
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Aamina Herring

Given:
$\underset{\left(x,y\right)\to \left(2,0\right)}{lim}\frac{1-\mathrm{cos}y}{x{y}^{2}}$
we will choose $y=mx$ when .
$\underset{\left(x,y\right)\to \left(2,0\right)}{lim}\frac{1-\mathrm{cos}y}{x{y}^{2}}$
$=\underset{x\to 0}{lim}\frac{1-\mathrm{cos}\left(mx\right)}{x\left(mx{\right)}^{2}}$
$=\underset{x\to 0}{lim}\frac{m\mathrm{sin}mx}{3{m}^{2}{x}^{2}}$
$=\underset{x\to 0}{lim}\frac{m\mathrm{cos}mx}{6mx}$
$=\underset{x\to 0}{lim}\frac{-m\mathrm{sin}mx}{6}$
$=0$

Jeffrey Jordon