(b) Find the areas under the graphs of f and g from x = 1 to x = t and evaluate for t 10, 100, 104, 106, 10¹0, and 1020. (Round your answers to two decimal places.)area under the graph of farea under the graph of gt1010010410610101020F(t)(c) Find the total area under each curve for x ≥ 1, if it is exists. (Round your answers to one decimal place.)total area under the graph of fG(t)total area under the graph of g A graphing calculator is recommended.(a) Graph the functions f(x)1.00.8Viewing window [0, 10] by [0, 1]:CHOICE Ay0.60.40.2CHOICE Cy1.0=20.94x¹.1and g(x):4f(x)g(x)=60.94in the viewing rectangles [0, 10] by [0, 1] and [0, 100] by [0, 1].+0.9810XiCHOICE By1.00.80.60.40.2CHOICE Dy1.024f(x)g(x)6810X

Given a list of questions:Using a graphing calculator we need to graph the functions in the…

Answered: graphing calculator is recommended. (a)…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.5: Graphs Of Functions

Problem 58E

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Related questions

Question

(b) Find the areas under the graphs of f and g from x = 1 to x = t and evaluate for t 10, 100, 104, 106, 10¹0, and 1020. (Round your answers to two decimal places.)
area under the graph of f
area under the graph of g
t
10
100
104
106
1010
1020
F(t)
(c) Find the total area under each curve for x ≥ 1, if it is exists. (Round your answers to one decimal place.)
total area under the graph of f
G(t)
total area under the graph of g

A graphing calculator is recommended.
(a) Graph the functions f(x)
1.0
0.8
Viewing window [0, 10] by [0, 1]:
CHOICE A
y
0.6
0.4
0.2
CHOICE C
y
1.0
=
2
0.94
x¹.1
and g(x):
4
f(x)
g(x)
=
6
0.94
in the viewing rectangles [0, 10] by [0, 1] and [0, 100] by [0, 1].
+0.9
8
10
X
i
CHOICE B
y
1.0
0.8
0.6
0.4
0.2
CHOICE D
y
1.0
2
4
f(x)
g(x)
6
8
10
X

Expert Solution

Step 1: Introduction to the problem and concepts used:

Given a list of questions:

Using a graphing calculator we need to graph the functions $f left parenthesis x right parenthesis equals fraction numerator 0.94 over denominator x to the power of 1.1 end exponent end fraction$ in the rectangle [0, 10] by [0,1] and $g left parenthesis x right parenthesis equals fraction numerator 0.94 over denominator x to the power of 0.9 end exponent end fraction$ in the rectangle [0,100] by [0,1] with viewing window [0,10] by [0,1].
Need to find the area under the curves f and g from x=1 to x=t. Evaluate the values of both the functions at points $t equals 10 comma space comma 100 comma space 10 to the power of 4 comma space 10 to the power of 6 comma space 10 to the power of 10 comma space 10 to the power of 20$ and round off it to two decimal places.
Need to find the total area under each curve for $x greater or equal than 1$ if it exists and round off it to one decimal place.

Function: A function is a mathematical relationship between two sets of numbers, such that each member of the first set is associated with exactly one member of the second set. The first set is called the domain of the function, and the second set is called the range of the function.

Graph: The graph of a function is a visual representation of the relationship between the domain and range of the function. It is a collection of points in the coordinate plane, where each point represents a member of the domain and its associated member of the range.

The Area under the graph: The definite integral is a more rigorous way of calculating the area under the graph of a function. The definite integral uses the fundamental theorem of calculus to calculate the area from x=a to x=b under the graph of a function f(x).

The formula for the definite integral to find the area:

$A equals integral subscript a superscript b f left parenthesis x right parenthesis d x$