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  -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 ≤ 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 ≤ 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.

... step-by-step information on finding probabilities using ... claim to consistently driver over the legal speed limit. ...Find the probability that, in a random sample ...

... b) Sketch the graph of the cosine function h(x) = cos x. What is the slope of the tangent line at the point (0,1)? Use limits to find this slope analytically. ...

...Find the dimensions of the rectangle with the greatest area that can be built so the base of ... calculate the limit of each expression as "x→ ∞." (7x+12)/(3x-2 ...

... 2. σ is known 3. Scores are sampled randomly and are independent You find that there are considerable overlaps in the limits and so the senior accountant ...

...Finding Sample Size ... error, confidence level, and population standard deviation σ to find the minimum ... If the difference for each day is found by subtracting the ...

... we can narrow down the problem to finding this limit: ... what we were looking for and what we found using l ... be differentiable using L'Hopital's Rule to find a limit...

Finding Probability and Confidence Intervals. ... Interval Interval Lower Limit 12.16 Interval Upper Limit 13.24. ... scouts are selected at random, find the probability ...

... attempt to find a volume for this object by first finding the volume of the bounded object in terms of the right hand bound, then trying to take the limit as ...