Limit = x-->infinity
11x^5+4x^3-6x+2/6x^3+5x^2+3x-1
My work:
After doing lots of work I got
11/x^2 +4 -6/x^2 +2/x^3
All over 6+5/x+3/x^2-1/x^3
So then I get 4/6 but the correct answer is supposed to be infinity.. I'm very confused
whenever the numerator has higher degree than the denominator, the limit will be infinity.
the usual method to show this is to divide top and bottom by the highest power anywhere.
11x^5+4x^3-6x+2
--------------------
6x^3+5x^2+3x-1
11 + 4/x^2 - 6/x^4 + 2/x^5
-----------------------------------
6/x^2 + 5/x^3 + 3/x^4 - 1/x^5
All those terms with powers of x in the bottom --> 0 as x --> infinity. So, you are left with
11/0 = infinity
This is also usually given a simplified argument. As x gets huge, only the highest power matters. So, the complicated fraction is really just
11x^5/6x^3 = 11/6 x^2 --> infinity