BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 2.2, Problem 7E
To determine

To sketch: The graph of f(x) and determine the value of a from the graph for which limxaf(x) exists.

Expert Solution

Explanation of Solution

Given:

The function f(x)={1+xif x<1x2if 1x<12xif x1.

Graph:

Draw a parabola of y=x2 between the interval 1x<1 and draw a ray of y=2x starting at the point (1, 1) on a given interval x1 and draw a ray of y=2x on a interval x<1.

The graph of f(x) is shown below in Figure 1.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 2.2, Problem 7E

From Figure 1, it is observed that graph has a parabola with center (0,0) and passing through the points (1,1) and (1,1). Moreover, the graph has a ray which starts at (1,1).

Notice that the left-sided limit and the right-sided limit are not same when a=1.

That is, limx1f(x)limx1+f(x).

Therefore, it can be concluded that limxaf(x) exists for every value of a excluding at the point a=1.

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!