Answer:
0
Step-by-step explanation:
The given limit is
[tex]\lim_{x \to \infty} \frac{x^2+x-22}{4x^3- 13}[/tex]
Divide both the numerator and the denominator by the highest power of x in the denominator.
[tex]=\lim_{x \to \infty} \frac{\frac{x^2}{x^3}+\frac{x}{x^3}-\frac{22}{x^3}}{\frac{4x^3}{x^3}- \frac{13}{x^3}}[/tex]
This simplifies to;
[tex]=\lim_{x \to \infty} \frac{\frac{1}{x}+\frac{1}{x^2}-\frac{22}{x^3}}{4- \frac{13}{x^3}}[/tex]
As [tex]x\to \infty, \frac{c}{x^n} \to 0[/tex]
[tex]=\lim_{x \to \infty} \frac{0+0-0}{4- 0}=0[/tex]
The limit is zero
