Question

lim= (X⁵ + 3X² + 3) / (99X² + 44X + 13)

(x→∞)

Answer 1

$\lim \limits_{x\to \infty} \frac{x^5+3x^2+3}{99x^2+44x+13}=\lim \limits_{x\to \infty} \frac{1+\frac{3}{x^3}+\frac{3}{x^5}}{\frac{99}{x^3}+\frac{44}{x^4}+\frac{13}{x^5}}=\infty$

As we know $\lim \limits_{x\to \infty} \frac{1}{x^n}=0,$ where $n=1,2,3,4,....$ . So expressions in the numerator and denominator in our expression go to zero. But in denominator it goes to zero faster. Therefore, the expression increases indefinitely.