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Finding a Limit

Find limit x>> -1^+ f(x)

f(x)= x - 2, for x <= 3; x - 1, for x > 3

Also: When you first begin to draw the graph of f(x), why do you start where you do? How high do I go when drawing a graph? How do I know when to stop?

Solution Preview

We want to find the limit of f(x) as x approaches -1 from the right. (Limit x &#61664; -1 means that we're looking at what happens to f(x) as x approaches -1, and the + next to the -1 means we're interested in the limit from the right, not from the left.)

f(x)= x - 2, for x &#8804; 3; x - 1, for x > 3

Let's draw the graph first, then we can use the graph to find the limit. I'll tell you what I'm doing step-by-step.

We know that f(x) = x - 2, for x &#8804; 3. Because this is valid for all values of x less than 3 AND when x = 3, we might as well start with x = 3. Plug x = 3 into the equation: f(3) = 3 - 2 = 1. Therefore, there is a point at (3, 1). Draw that on the graph. (I'm trying to be as accurate as possible. If you make a graph by hand it will probably look better.)

Now, look at ...

Solution Summary

The solution explains how to find the limit of the function and how to graph the function in a meaningful way.