Calculus: Graphical, Numerical, Algebraic: Solutions Manual

3rd Edition

ISBN: 9780132014144

Author: Ross L. Finney, Franklin Demana, Bert K. Waits, Daniel Kennedy

Publisher: Pearson Prentice Hall

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Differential Equations

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Question

Chapter 1, Problem 40RE

To determine

To find: The piece-wise formula for the given graph of the function.

Expert Solution & Answer

Answer to Problem 40RE

The required piece-wise function is f(x)={52x, 0≤x<210−52x, 2≤x≤4 .

Explanation of Solution

Given information: The given graph of the function is,

Calculus: Graphical, Numerical, Algebraic: Solutions Manual, Chapter 1, Problem 40RE

Calculation:

The piece-wise function is divided into two parts.

For the interval x∈[0,2) , from the graph it can be seen that the line passes through the points (0,0) and (2, 5) .

The equation of line passes through two points is calculated as:

y−0=5−02−0(x−0)y=52x

For the interval x∈[2, 4] , from the graph it can be seen that the line passes through the points (2, 5) and (4, 0) .

The equation of line passes through two points is calculated as:

y−5=0−54−2(x−2)y−5=−52(x−2)y−5=−52x+5y=10−52x

Therefore, the required piece-wise function is f(x)={52x, 0≤x<210−52x, 2≤x≤4 .

Chapter 1, Problem 39RE

Chapter 1, Problem 41RE

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic: Solutions Manual

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

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