I have the equation below:
$$ lim_{x\to \infty} \frac{\sqrt {4x^2+4x}}{4x+1} $$
The hint provided to solve this problem is as below:
To do that, we will want to divide both the numerator and the denominator by the same quantity, in a way that will help us derive the limit.
Since the leading term of the denominator is $x$, let's divide by $x$.
In the numerator, let's divide by $\sqrt {x^2}$, since for positive values, $x = \sqrt {x^2}$.
$$ lim_{x\to \infty} \frac{\sqrt {4x^2+4x}}{4x+1} $$ $$ lim_{x\to \infty} \frac {\frac{\sqrt {4x^2+4x}}{\sqrt {x^2}}} {\frac{4x+1}{x} } $$
Can you show me how the values $x = \sqrt {x^2}$? I'd like to see the proof. Thank you.