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Chapter 4: Problem 11

Sketch the region that corresponds to the given inequalities, say whether the region is bounded or unbounded, and find the coordinates of all corner points (if any). $$ x \geq-5 $$

Short Answer

Expert verified
The region corresponding to the inequality \(x \geq -5\) is the area to the right of the vertical line at \(x = -5\), including the line itself. This region is unbounded, with no corner points.

Step by step solution

01

Graphing the inequality

To graph the inequality \(x \geq -5\), plot a vertical line at \(x = -5\). Since the inequality is greater than or equal to \(-5\), the region that satisfies the inequality would be the area to the right of this vertical line, which includes the line itself.
02

Identifying the properties of the region

In this case, our region extends infinitely to the right of the vertical line at \(x = -5\). This makes our region unbounded, meaning it doesn't have a finite maximum or minimum value.
03

Identify any corner points

Since the region is unbounded, there are no corner points as the region stretches infinitely in various directions (up, down, and right) from the line \(x = -5\). To summarize, the region that corresponds to the given inequality is the area to the right of the vertical line at \(x = -5\), including the line itself. The region is unbounded, and there are no corner points.

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Most popular questions from this chapter

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