Answer:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{4x^2 + 4x}}{4x + 1} = 1[/tex]
General Formulas and Concepts:
Calculus
Limits
Coefficient Power Method: [tex]\displaystyle \lim_{x \to \pm \infty} \frac{ax^n}{bx^n} = \frac{a}{b}[/tex]
Step-by-step explanation:
We are given the limit:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{4x^2 + 4x}}{4x + 1}[/tex]
We can see that if we "simplify" the radical, resulting in a degree of 1. Let's use Coefficient Power Method to evaluate the limit:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{4x^2 + 4x}}{4x + 1} = \frac{4}{4}[/tex]
Simplifying it:
[tex]\displaystyle \lim_{x \to \infty} \frac{\sqrt{4x^2 + 4x}}{4x + 1} = 1[/tex]
And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
