Q. 12 - Calculus

Question

Explain why the inequality $0\le r\le 2$ describes the points inside or on the circle with radius 2 and centered at the origin. Use a similar inequality to describe the points in the annulus shown here:

Step-by-Step Solution

Answer

The answer is Inside the circle , $0\le r\le 1$with radius 1 .

Step 1: Given information

The inequality $0\le r\le 2$

Step 2: Simplification

Consider the inequality $0\le r\le 2$ of the annulus.

The objective is to show an inequality to describe the points in the annulus. The given annulus is with center $(0,0)$ and of radius 4 .

\

The inequality $0\le r\le 2$ represents a circle with radius 2 .

Thus, the points of the inequality represent the values less than 2 which are inside the circle.

Now the inequality $0\le r\le 1$ represents a circle with radius 1 and the values of the inequality lies inside the circle.

Thus, the inequality $0\le r\le 2$ describes the points inside the circle with radius 2 .

The inequality $0\le r\le 1$ describes the points inside the circle with radius 1 .

Therefore, the answer is Inside the circle ,$0\le r\le 1$ with radius 1 .