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 1.1, Problem 50E
To determine

To find: An expression for the function whose graph is the top half of the circle x2+(y2)2=4.

Expert Solution

Answer to Problem 50E

The function of the top half of the circle x2+(y2)2=4 is f(x)=2+4x2_ where 2x2.

Explanation of Solution

Given:

The graph is the top half of the circle x2+(y2)2=4.

Calculation:

Solve the equation of the circle x2+(y2)2=4 and solve for y.

x2+(y2)2=4(y2)2=4x2y2=±4x2y=2±4x2

Since the graph is the top half of the circle, consider the root with a positive radical. Therefore, the function of the top half of the circle is f(x)=2+4x2.

The expression inside the square root cannot be negative. This implies,

4x204x2±2x

Thus, the domain is 2x2.

Therefore, the function of the top half of the circle x2+(y2)2=4 is f(x)=2+4x2_ where 2x2.

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