Find the vertical asymptotes and then determine the left and right limits at each vertical asymptote.

Question

Find the limit: lim f(x) if exists.

x-->c

F(x)=(x-1)/x²(x-2)

Answer 1

For rational functions, to find the vertical asymptotes, we find what makes the denominator zero because since division by zero is undefined, there are is possible y value for those x-values (thus an asymptote). In this case, the denominator is zero for x = 0 and x = 2.

Looking at the graph, we see this:

We can see that the limits as x → 0 and x → 2 DNE however, we could say