Question

Să se calculeze următoarea limită, vă rog!

Answer 1

Răspuns:

$\lim_{x \to 4} \frac{\sqrt{x-3}-1}{\sqrt{x+5}-3 }= \lim_{x \to 4} \frac{\frac{(\sqrt{x-3}-1)(\sqrt{x-3}+1)}{\sqrt{x-3}+1} }{\frac{(\sqrt{x+5}-3)(\sqrt{x+5}+3)}{\sqrt{x+5}+3}  }=\lim_{x \to 4} \frac{\frac{x-3-1}{\sqrt{x-3}+1} }{\frac{x+5-9 }{\sqrt{x+5}+3} }=\lim_{x \to 4} \frac{\frac{x-4}{\sqrt{x-3}+1}}{\frac{x-4}{\sqrt{x+5}+3} }=\lim_{x \to 4} \frac{\frac{1}{\sqrt{x-3}+1}}{\frac{1}{\sqrt{x+5}+3} }=\lim_{x \to 4} \frac{\sqrt{x+5}+3}{{\sqrt{x-3}+1} }=\frac{6}{2} =3$

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