Limite

jhgfdrfchn;km

Seja \(\lim _{x\to 36}\left(\frac{\left(6-\sqrt{x}\right)}{36-x}\right)\)

Vamos racionalizar usando \(\frac{6+\sqrt{x}}{6+\sqrt{x}}\)

\(\lim _{x\to 36}\left(\frac{\left(6-\sqrt{x}\right)}{36-x}\right)=\lim _{x\to 36}\left(\frac{\left(6-\sqrt{x}\right)}{36-x}\right.\frac{6+\sqrt{x}}{6+\sqrt{x}})\)

\(\lim _{x\to \:36}\left(\frac{1}{6+\sqrt{x}}\right)\)

\(\lim _{x\to \:36}\left(\frac{1}{6+\sqrt{x}}\right)=​​\lim _{x\to \:36}\left(\frac{1}{6+\sqrt{36}}\right)\\ ​​\lim _{x\to \:36}\left(\frac{1}{6+\sqrt{36}}\right)=\frac{1}{12}\)

Portanto:

\(\boxed{\lim _{x\to 36}\left(\frac{\left(6-\sqrt{x}\right)}{36-x}\right)=\frac{1}{12}}\)