Verified answer

There is another way of solving this for the limit when x->inf

Multiplying the nominator and denominator by 1/x^3, you will get:

lim(x-> inf) (10+4/x)/(8-4/x^3)

Note that when x-> inf, 4/x and 4/x^3 goes to 0.

So the whole limit will goes to 5/4.

You can also do this with L'Hospital's Rule, but you need to differentiate quite a lot of time. By using the method I mentioned, you can save time and still get the same answer. Note that this method can be used when x-> inf.