Răspuns:
[tex]\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[/tex]
Explicație pas cu pas:
