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Consider the following expression.$$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$$The value of the above expression (rounded to 2 decimal places) is ___________.
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$\displaystyle \lim_{x \to -3} \frac{\sqrt{2x+22}\,-4}{x+3}\; (\frac{0}{0}\,form)$

$\text{Using L'Hôpital's rule}$

$\displaystyle \lim_{x \to -3} \frac{\frac{1}{2\sqrt{2x+22}}(2)\,-0}{1+0} =\lim_{x \to -3}\frac{1}{\sqrt{2x+22}} =\frac{1}{\sqrt{2(-3)+22}} =\frac{1}{4}=0.25$
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