Evaluate the limit:
Lim [(2x+1)^3 (x-3)] / (x^2 + 1)^2
x->infiniti
10 points to whoever solves it first (or is helpful to me in solving it)
PS: show work plz
2007-10-07 06:59:46 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Multiply things out:
Lim(8x^4+4x^3-6x^2-5x-1)/(x^4+2x^2 +1)
x --> infinity
Now divide both numerator and denominator by x^4.
You will immediately see that the limit is 8/1 = 8
2007-10-07 07:16:09 · answer #1 · answered by ironduke8159 7 · 0⤊ 0⤋
This kind of problem has a polynomial in the numerator and a polynomial in the denominator. We do not need to simplify the polynomials we just need to determine the term with the highest degree.
The (2x +1)^3 is just taken as (2x)^3 which is 8x^3. The (x-3) is just taken as x so the final product is 8x^4
For the bottom (x^2 +1)^2 becomes (x^2)^2 which is x^4
So for the purpose of finding a limit the expression becomes
8x^4 / x^4
x->infinity
2007-10-07 14:23:31 · answer #2 · answered by Roy E 4 · 0⤊ 0⤋