Zadatak 0946

Test: MDsIVBGI_169

 

Izračunaj graničnu vrednost: $$\lim \limits_{x \to 65}\frac{\sqrt{x-1}-8}{\sqrt[3]{x-1}-4}$$

 

Rešenje:


$$...=\lim \limits_{x \to 65}\frac{\sqrt{x-1}-8}{\sqrt[3]{x-1}-4}\cdot \frac{\sqrt{x-1}+8}{\sqrt{x-1}+8}\cdot\frac{\sqrt[3]{(x-1)^2}+4\sqrt[3]{x-1}+16}{\sqrt[3]{(x-1)^2}+4\sqrt[3]{x-1}+16} $$

$$= \lim \limits_{x \to 65}\frac{x-1-64}{x-1-64}\cdot \frac{\sqrt[3]{(x-1)^2}+4\sqrt[3]{x-1}+16}{\sqrt{x-1}+8}$$

$$=\frac{48}{16}=3$$