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.

... an equation for the line tangent to the curve at the point x = 8. 6. Use one-sided limits to find the limit or determine that the limit does not exist 7. find...

... After several days of research, Bob finds that the ... Questions: 1. Find the sample mean and sample standard ... 2. When finding a confidence interval for the true ...

... This is 2 tailed because we are finding the margin ... Since it is very expensive to find successors of employees ... of small businesses with Web sites found that the ...

... next person to engage in hopes of finding information ... spend our time together describing your key findings on your ... get your training, how did you find out about ...

... We need to find z such that P(-z<Z<z)=0.5. By checking standard normal tableļ¼z=0.674. So when z=(x-mu)/sigma=(x-1500)/150=-0.674. x has lower limit which ...

... 0.2565/5208)= 0.0156 Upper limit: 0.7435+0.0156=0.7591 Lower limit: 0.7435-0.0156 ... Find the minimum sample size needed, using a prior study that found that 30 ...

...Find the indicated sum; a. b. c. d. Use properties of limits to find the indicated limit. ... Use properties of limits to find the indicated limit. ...

1. Compute the derivative of the given function and find the slope of the line ... (Compute the derivative of the function from the definition only, using limits. ...

... Confidence Interval Interval Lower Limit -6.01669889 Interval Upper Limit 30.81669889 Suppose that the ...Find the mean and the standard deviation of the sampling ...