Why is the difference between these two functions a constant?
Since the denominators are equal and the numerators differ in degree I would never have thought the difference of these functions would be a constant.
Of course I can calculate it is true: the difference is 2, but my intuition is still completely off here. So, who can provide some intuitive explanation of what is going on here? Perhaps using a graph of some kind that shows what’s special in this particular case?
BACKGROUND: The background of this question is that I tried to find this integral:
As a solution I found:
Whereas my calculusbook gave as the solution:
I thought I made a mistake but as it turned out, their difference was constant, so both are valid solutions.
Would you be surprised that the difference of 2x2+x+1x2 and x+1x2 is 2?