Precalc Help for Homework

Question

For the function y= ((30x+2)/(x^2+x-51)) , as x approaches positive infinity what is y approaching?

Answer 1

Divide each term by x² to get lim x→∞ (30x/x² +2/x²) /(x²/x² +x/x² -51/x²) which gives lim x→∞ (30/x +2/x²)/ (1+1/x -51/x²). Take the limit x→∞ gives (0+0)/(1+0-0) and the limit is 0. So y→0 when x→∞.