First of all, thank you for sharing the illustration of this problem. Without the illustration it would be hard to come up with an answer, since there are various kinds of limit and your own, typewritten instructions did not specify which.
Here you're finding the limit as x approaches infinity. Both 2x and 4x (as shown in the illustration grow larger continually and without bound, as x increases. As this happens, the other terms (+3 and -5) are simply overpowered by the x terms. If you choose to ignore these other terms for this reason, then your expression will be
2x
----- and this approaches the value 1/2 as x grows increasingly large in the
4x original expression.
So the limit of that expression, as x grows large without bound, is 1/2.
