   Chapter 5.5, Problem 28E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding the Area Bounded by Two Graphs In Exercises 15-30, sketch the region bounded by the graphs of the functions and find the area of the region. See Examples 1, 2, 3, and 4. f ( x ) = 1 x ,   g ( x ) = − e x , x = 1 2 , x = 1

To determine

To graph: The region bounded by the graphs of f(x)=1x, g(x)=ex, x=12 and x=1, and also compute the area of the region.

Explanation

Given Information:

The region bounded by the graphs of f(x)=1x, g(x)=ex, x=12 and x=1.

Graph:

Consider the following equations that give the required region,

f(x)=1x, g(x)=ex, x=12 and x=1

Then the first function f(x)=1x is a reciprocal function. The graph will lie in first and third quadrant. As x increases in both directions, y will decrease and vice-versa. There will be no x-intercept and no y-intercept.

Now the second function g(x)=ex is an exponential function with positive exponent and negative co-efficient. So, the value of y will always be negative and the graph will lie in third and fourth quadrants.

There will be no x-intercept and no y-intercept.

The intersecting points of x=2 and f(x)=1x.

y=1x=12

The intersecting points of x=1 and f(x)=1x.

y=1x=1

And

The intersecting points of x=2 and g(x)=ex.

g(x)=ex=e12y=1.649

Similarly, the intersecting points of x=1 and g(x)=ex.

g(x)=e1=e1y=2.718

The intersecting points are, (12,2),(12,1.649),(1,1),(1,2.718).

Sketch the graph of the region as follows:

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