Finding a limit by looking at the function

Question

Find the indicated limit, if it exists. (If an answer does not exist, enter DNE.)

lim

(x->infinity)

 

((24 x^4 - x^3 + x + 8)/(8 x^4 + 2 x^3 + x^2 + 5x + 14))

Answer 1

This is very easy because when the degrees of the two polynomials are equal, the limit as x goes to infinity is equal to the ratio of the leading coefficients.

 

Answer:  24/8 = 3.