Answer:
[tex]\displaystyle \lim_{x \to -\infty} \frac{5x^2 + 6x}{\sqrt{16x^4 - 5x^2}} = \frac{5}{16}[/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{5x^2 + 6x}{\sqrt{16x^4 - 5x^2}}[/tex]
We can see that if we "simplify" the radical, resulting in a degree of 2. Let's use Coefficient Power Method to evaluate the limit:
[tex]\displaystyle \lim_{x \to -\infty} \frac{5x^2 + 6x}{\sqrt{16x^4 - 5x^2}} = \frac{5}{16}[/tex]
And we have our answer.
Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
