# Use and cite the continuity theorems presented in lecture to find and justify th

Use and cite the continuity theorems presented in lecture to find and justify the limit.
$\underset{x\to 0}{lim}\left[{e}^{\mathrm{sin}\left(x\right)}+\frac{{x}^{2}}{x-2}\right]$
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Given:
$\underset{x\to 0}{lim}\left[{e}^{\mathrm{sin}\left(x\right)}+\frac{{x}^{2}}{x-2}\right]$
Put the value of x=0
$\underset{x\to 0}{lim}\left[{e}^{\mathrm{sin}\left(x\right)}+\frac{{x}^{2}}{x-2}\right]=\underset{x\to 0}{lim}{e}^{\mathrm{sin}x}+\underset{x\to 0}{lim}\frac{{x}^{2}}{x-2}$
$={e}^{\mathrm{sin}\left(0\right)}+\frac{{0}^{2}}{0-2}$
$={e}^{0}+\frac{0}{-2}$
$=1+0$
$=1$
Answer: is equal to $\underset{x\to 0}{lim}\left[{e}^{\mathrm{sin}x}+\frac{{x}^{2}}{x-2}\right]=1$
Jeffrey Jordon