given the function: f(x) = (x^{2}) / (x1) the correct answer to the limit of f(x) as x approaches infinity is: y = x+1 all math references point to this answer and the method they all use is long division of x1 into x^{2} however if one were to multiply both the numerator and denominator by 1/x and then take the limit, one gets: y=x how can the descrepency between the two answers be explained? Frank Hi Frank,Your approach of multiplying numerator and denominator by 1/x shows that the limit of x^{2}/(x1) goes to infinity as x goes to infinity. There's really not much difference between infinity and (infinity + 1). To show that y = x+1 is an asymptote of the curve c: y = x^{2}/(x1) as x goes to infinity you need to show that the graph of the line y = x+1 approaches the graph of the curve, which it does. If you don't believe me, look at the difference (for fixed x) between x1 and c, and you will see that the difference approaches 0 as x goes to infinity. This is the argument given in the math references you saw. The difference between x and c approaches 1. Other methods: You can (a) let y = x1 (so that x = y+1) and change the given function into an expression involving y that is easier to divide by. (You'll find that the limit is y+2, which equals x1.) or (b) Put the expression ax + b  [x^{2}/(x1)] over a common denominator, then set the numerator = 0 and solve for a and for b. (You'll find that a=1 and b=1.) Chris and Penny
