Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

4th Edition

ISBN: 9780133178579

Author: Ross L. Finney

Publisher: PEARSON

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Question

Chapter 1.2, Problem 47E

To determine

To find: The piecewise formula for the given function.

Expert Solution & Answer

Answer to Problem 47E

The piecewise function for the given graph of function is y={0, 0≤x≤T22Tx−1, T2<x≤T.

Explanation of Solution

Given information:

The graph of the function is:

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy), Chapter 1.2, Problem 47E

Calculation:

The graph of the function consists of two straight lines passing through the points (0,0) , (T2,0) and (T2,0) , (T,1) respectively.

Use the formula for the slope of line that passes through (0,0) and (T2,0).

m=y2−y1x2−x1=0−0T2−0=0

The equation of the line passing through the points (0,0) and (T2,0).

y−y0=m(x−x0)y−0=0(x−0)y=0

So, the equation of the first line is y=0 defined for 0≤x≤T2.

Use the formula for the slope of line that passes through (T2,0) and (T,1).

m=y2−y1x2−x1=1−0T−T2=1T2=2T

The equation of the line passing through the points (T2,0) and (T,1).

y−y0=m(x−x0)y−0=2T(x−T2)y=2Tx−1

So, the equation of the second line is y=2Tx−1 defined for T2≤x≤T.

Therefore, the piecewise function for the given graph of function is y={0, 0≤x≤T22Tx−1, T2<x≤T.

Chapter 1.2, Problem 46E

Chapter 1.2, Problem 48E

Chapter 1 Solutions

Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)

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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