# Evaluate the following limits. lim_{xrightarrow-3}frac{sin(x+3)}{x^2+8x+15}

Emeli Hagan 2021-02-18 Answered
Evaluate the following limits.
$\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{{x}^{2}+8x+15}$
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averes8
To evaluate
$\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{{x}^{2}+8x+15}$
Using, $\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{{x}^{2}+8x+15}=\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{{x}^{2}+3x+5x+15}$
$=\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{x\left(x+3\right)+5\left(x+3\right)}$
$=\underset{x\to -3}{lim}\frac{\mathrm{sin}\left(x+3\right)}{\left(x+3\right)\left(x+5\right)}$
$=\underset{h\to 0}{lim}\left[\frac{\mathrm{sin}h}{h}×\frac{1}{h+2}\right]$
$=\frac{1}{2}$
Jeffrey Jordon