# What is the limit of #[3 + 4/x - 5/x^2 + [x-1]/[x^3+1]# as x goes to infinity?

##### 2 Answers

Oct 24, 2015

3

#### Explanation:

Every term in the expression

The reason is that the other terms are rational functions where the denominator has a higher degree than the numerator.

Jul 27, 2016

If we actually took the limit, we can separate each term. Since each of these functions have existent limits...

#color(blue)(lim_(x->oo) 3 + 4/x - 5/x^2 + (x-1)/(x^3+1))#

#= lim_(x->oo) 3 + lim_(x->oo) 4/x - lim_(x->oo) 5/x^2 + lim_(x->oo) (x-1)/(x^3+1)#

As

#=> 3 + cancel(4/(oo))^(0) - cancel(5/(oo))^(0) + cancel(lim_(x->oo) 1/(x^2))^(1/(oo) -> 0)#

#= color(blue)(3)#