Question

Calculus: Evaluate Lim as x approaches infinty f(x) and Lim as x approaches negative infinity f(x) for the function: f(x)=(x^3 +6)/(3x^3) + √(36x^6 +2)

Answer 1

if all that stuff is in the denominator, it will be 1/9

Answer 2

Yes all of it on the right is in the denominator

Answer 3

that is, if the denominator is
\[3x^3+\sqrt{36x^6+2}\] numerator has degree three and while the denominator is not a polynomial the +2 under the radical is irrelevant, and so it behaves like
\[3x^3+6x^3=x^3\] so you have
\[\frac{x^3}{9x^3}=\frac{1}{9}\] as x goes to infinity

Answer 4

Good answer, but why is the +2 in denominator and +6 in numerator irrelevant?