BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 1, Problem 14T

(a)

To determine

To solve: The solution of equation x39x1=0 through graph.

Expert Solution

Answer to Problem 14T

Solution:

The solutions of equation x39x1=0 are x=2.94 , 0.11 and x=3.05 .

Explanation of Solution

The given equation is,

x39x1=0

In the above equation let the left-hand side equation is,

y=x39x1

The graphs of equation y is shown below,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 14T , additional homework tip  1

Figure (1)

The given equation is equivalent to y=0 and the solution is x-coordinate of intersection point of two graphs.

From Figure (1) the graph of y is equal to zero when graph intersect x-axis at x=2.943 , x=0.111 , x=3.054 approximately and these values of x-coordinates give the solution of given equation.

Thus, the solutions of equation x39x1=0 are x=2.94 , 0.11 and x=3.05 .

(b)

To determine

To solve: The solution of inequality x21|x+1| through graph.

Expert Solution

Answer to Problem 14T

The solution of inequality x21|x+1| is the interval [1,2] .

Explanation of Solution

The given inequality is,

x21|x+1|

In the above equation let left-hand equation is,

y1=x21

The right-hand side equation is,

y2=|x+1|

The graph of equation y1 and y2 on the same set of axis is shown below.

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 1, Problem 14T , additional homework tip  2

Figure (2)

The given equation is equivalent to y1y2 and the solution of inequality is all x-values for which the graph of y1 is less than or equal to y2 .

From Figure (2) the graph of y1 and y2 intersects each other at points (1,0) and (2,3) in which the values of x-coordinates are 1 , 2 and the graph of y1 is on or below the graph y2 when values of x lie in between x=1 to x=2 and these values of x-coordinates give the solution of given inequality.

Thus, the solution of inequality x21|x+1| is the interval [1,2] .

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