Question

What is the limit of `(4x)/(x-6)+(5x)/(x+6)` as x approaches infinity?

Answer 1

The limit is `9`

Explanation:

`lim_(xrarroo)(4x)/(x-6) = lim_(xrarroo)(4x)/(x(1-6/x))`

`= lim_(xrarroo)(4)/((1-6/x)) = 4/(1-0) = 4`

And

`lim_(xrarroo)(5x)/(x+6) = lim_(xrarroo)(5x)/(x(1+6/x))`

`= lim_(xrarroo)(5)/((1+6/x)) = 5/(1+0) = 5`

Therefore,

`lim_(xrarroo)((4x)/(x-6) + (5x)/(x+6)) = lim_(xrarroo)(4x)/(x-6) + lim_(xrarroo)(5x)/(x+6)`

`= 4+5=9`