Limit

Problem:

Solution:

$ \lim\limits_{x \to \infty}{\frac{\sqrt{4x + 4x^2}}{4x + 5}} $
= $ \lim\limits_{x \to \infty}{\frac{\frac{\sqrt{4x + 4x^2}}{x}}{\frac{4x + 5}{x}}} $
= $ \lim\limits_{x \to \infty}{\frac{\sqrt{\frac{4x + 4x^2}{x^2}}}{\frac{4x + 5}{x}}} $
= $ \lim\limits_{x \to \infty}{\frac{\sqrt{\frac{4}{x} + 4}}{4 + \frac{5}{x}}} $
= $ \frac{\sqrt{4}}{4} $
= $ \frac{1}{2} $