Evaluate Limit: 3x^3 + x + 26 / 20x^2 - 5x^3

[rcmango]

Homework Statement

Evaluate the Limit.

lim x -> infinity (3x^3 + x + 26) / (20x^2 - 5x^3)

Homework Equations

The Attempt at a Solution

I found the answer to be -3/5. is this correct?
I just divided the numerator and the denominator by the greatest exponent.
I see how it was done, but what are the rules to such a problem, and maybe someone could explain what is really going on here. Thankyou.

 

[olgranpappy]

Homework Statement

Evaluate the Limit.

lim x -> infinity (3x^3 + x + 26) / (20x^2 - 5x^3)

Homework Equations

The Attempt at a Solution

I found the answer to be -3/5. is this correct?

yes.

I just divided the numerator and the denominator by the greatest exponent.
I see how it was done, but what are the rules to such a problem, and maybe someone could explain what is really going on here. Thankyou.

to just look and see is the best way. If you wanted, I guess you could have used L'Hopital's Rule:

f=3x^3 + x + 26
g=20x^2 - 5x^3

lim f/g -> inf/inf
lim f'/g' -> inf/inf
lim f''/g'' -> inf/inf
lim f'''/g''' -> -3/5

 

[rcmango]

okay i see, but in the original method, do i divide by the largest exponent in the numerator or the denominator, i know I divide the top and bottom by this exponent.

 

[Gib Z]

There is a general method for the limit of the quotient of 2 polynomials. Write out the quotient of a general polynomial of degree m, co efficients are a_m, a_{m-1}..., and then divide by another polynomial degree n, co efficients are b_n, b_{n-1}. There are 3 cases, 1) m > n, m=n and m< n. For every case, divide through by the highest exponent of x. What do you get?