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yan [13]
4 years ago
11

Lim x—> -2 sqrt(3x+10) -2/ x+2

Mathematics
1 answer:
snow_lady [41]4 years ago
8 0

\displaystyle\lim_{x\to-2}\frac{\sqrt{3x+10}-2}{x+2}

Rationalize the numerator:

\dfrac{\sqrt{3x+10}-2}{x+2}\cdot\dfrac{\sqrt{3x+10}+2}{\sqrt{3x+10}+2}=\dfrac{(3x+10)-4}{(x+2)(\sqrt{3x+10}+2)}=\dfrac3{\sqrt{3x+10}+2}

where the x+2 factors in the numerator and denominator cancel. Then the limit is

\displaystyle\lim_{x\to-2}\frac{\sqrt{3x+10}-2}{x+2}=\lim_{x\to-2}\frac3{\sqrt{3x+10}+2}=\frac3{\sqrt4+2}=\boxed{\frac34}

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