Answer:
(B) 3
Step-by-step explanation:
Qualitative answer. As x grows larger and larger, the contribute of lower degree terms (and constants) becomes irrelevant, and you rewrite everything picking the highest term for both numerator and denominator
[tex]\lim\limits_{x \to \infty} \frac{\sqrt{9x^4}}{x^2} $\lim\limits_{x \to \infty} \frac{3x^2}{x^2}=3[/tex]
Analitically.
Collect [tex]9x^4[/tex] in the numerator under the square root, [tex]x^2[/tex] in the denominator.
[tex]\lim\limits_{x \to \infty} \frac{\sqrt{9x^4(1+\frac{1}{9x^4})}}{x^2(1-\frac{3}{x}+\frac{5}{x^2})} = \lim\limits_{x \to \infty}\frac{3x^2\sqrt{(1+\frac{1}{9x^4})}}{{x^2(1-\frac{3}{x}+\frac{5}{x^2})}} = 3[/tex]
At this point the way you deal with it is the usual. Anything inside the bracket goes to 0 besides the lead coefficients (1 in both cases) and you're left with 3.
