Philip P. answered • 05/31/18

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f(x) = (x

^{2}-3x)/(x^{2}-9) = x(x-3)/(x+3)(x-3) = x/(x+3)f(x) has a vertical asymptote at x = -3, so the limits from each side will shoot to either plus or minus infinity. If you plug in a few values close to x = -3 from each side, say x = -3.01 from the left and x = -2.99 from the right, you'll see that the limit shoots to +∞ from the left and to -∞ from the right. Since the limits are not the same, there is no limit for f(x).

Use a graphing calculator or program to graph f(x) = x/(x+3) to confirm the behavior.