Question

2x^3+6x^2+5/3+x^2 lim x to infinity

Answer 1

Divide everything by the highest degree variable in the denominator.
In this case it is \(x^2\):\[
\lim_{x\to \infty}\frac{2x^3+6x^2+5}{3+x^2} = \lim_{x\to \infty}\frac{2x+6+\frac{5}{x^2}}{\frac{3}{x^2}+1}
\]

Answer 2

At this point you can plug in \(\infty\) and you will not have an indeterminate form.

Answer 3

wouldn't the highest degree be x^3? or does the numerator not count