Question

So I just have basic questions about limits which I just need to clear up. So when I'm solving for a limit , when the greater exponent is on the top of the fraction ex: x^2+2x/x+1 then the limit will always =infinity? And how do u know when a limit = 0 ? I just don't want to be confused on my exam tomrow, please help explain :)

Answer 1

yes, the limit is always ∞.The limit is Zero when the greater power is in the bottom.

This is because when x gets really huge, on;y the highest power counts. You can throw all the lower degree stuff away.

So,

3x^3-7x+3
------------ -> 3x^3/x = 3x^2 -> ∞
x+4

If the powers are the same, then the limit is just the ratio of the coefficients:

3x^3-7x+3
--------------- -> 3x^3/6x^3 = 1/2
6x^3+9x^2-3x+2

More formally, you can divide top and bottom by the biggest power, and then since k/x -> 0 as x->∞, all the fractions with x in the bottom -> 0 and can be discarded.

3x^3-6x^2+4
----------------
6x^4-2x+7

Divide all by x^4 and you have

3/x - 6/x^2 + 4/x^4
-------------------------
6 - 2/x^3 + 7/x^4

now let x->∞ and you are left with

(3/x)/6 -> 0/6 = 0

Answer 2

So when the greater power is on top, the limit will equal infinity and when it's on the bottom then it will equal 0?

Answer 3

Yes, I believe that is what I said in my first sentence.