Let P and Q be polynomials and consider the limit of P(x)/Q(x) as x approaches infinity. State and prove a conjecture for the value of this limit that depends on the degrees of P and Q and their leading coefficients.
Let P and Q be polynomials and consider the limit of P(x)/Q(x) as x approaches infinity. State and prove a conjecture for the value of this limit that depends on the degrees of P and Q and their leading coefficients.
Let and let .
If , then .
If , then .
If , then .
The proofs are fairly straightforward. If , just factor out from both polynomials and see what you have left.