Question

How do you evaluate `(3+10x)/(6x-10)` as x approaches infinity?

Answer 1

`lim_(xrarroo)(3+10x)/(6x-10)=5/3`

Explanation:

`lim_(xrarroo)(3+10x)/(6x-10)=lim_(xrarroo)((3+10x)/x)/((6x-10)/x)`
`=lim_(xrarroo)(3/x+10)/(6-10/x)`

We now observe that as `x->oo` then `3/x->0 and 10/x->0`

Hence, `lim_(xrarroo)(3+10x)/(6x-10)=10/6=5/3`

This can be visualized by looking at the graph for large `x`
graph{(3+10x)/(6x-10) [-10, 60, -5, 5]}