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High School Math Calculus PRECALCULUS:GRAPHICAL,...-NASTA ED.

a) To find: Draw the graph of the function for x in the specified interval and to verify that the function is non-negative in that interval. The graph of the function f x = x 2 in the interval 0 , 4 is, Given information: f x = x 2 in the interval 0 , 4 Calculation: Plotting the graph b) To find: Draw and shade the approximating rectangles for the RRAM and to find the area. The approximating rectangles for the RRAM and the area is, A ≈ 30 Given information: f x = x 2 in the interval 0 , 4 Calculation: The four sub-intervals are 0 , 1 , 1 , 2 , 2 , 3 , 3 , 4 For RRAM the upper right corners of the rectangles touch the graph of the function Each rectangles has a base of 1 while the heights are function value at the right-hand endpoint. A ≈ 1 + 4 + 9 = 14 Subintervals Base Height Area 0 , 1 1 f 1 = 1 2 = 1 1 1 = 1 1 , 2 1 f 2 = 2 2 = 4 1 4 = 4 2 , 3 1 f 3 = 3 2 = 9 1 9 = 9 3 , 4 1 f 4 = 4 2 = 16 1 16 = 16 c) To find: Draw and shade the approximating rectangles for the LRAM and to find the area. The approximating rectangles for the LRAM and the area is A ≈ 14 Given information: f x = x 2 in the interval 0 , 4 Calculation: For LRAM there is no rectangle in the interval 0.1 A ≈ 1 + 4 + 9 = 14 Subintervals Base Height Area 1 , 2 1 1 f 1 = 1 2 = 1 1 1 = 1 2 , 3 1 f 2 = 2 2 = 4 1 4 = 4 3 , 4 1 f 3 = 3 2 = 9 1 9 = 9 d) To find: Average area of RRAM and.LRAM. Average area of RRAM and.LRAM is 22 Given information: f x = x 2 in the interval 0 , 4 Calculation: Using RRAM the area is 30 and using LRAM the are is 14 the average estimate of the area is 30 + 14 2 = 22

a) To find: Draw the graph of the function for x in the specified interval and to verify that the function is non-negative in that interval. The graph of the function f x = x 2 in the interval 0 , 4 is, Given information: f x = x 2 in the interval 0 , 4 Calculation: Plotting the graph b) To find: Draw and shade the approximating rectangles for the RRAM and to find the area. The approximating rectangles for the RRAM and the area is, A ≈ 30 Given information: f x = x 2 in the interval 0 , 4 Calculation: The four sub-intervals are 0 , 1 , 1 , 2 , 2 , 3 , 3 , 4 For RRAM the upper right corners of the rectangles touch the graph of the function Each rectangles has a base of 1 while the heights are function value at the right-hand endpoint. A ≈ 1 + 4 + 9 = 14 Subintervals Base Height Area 0 , 1 1 f 1 = 1 2 = 1 1 1 = 1 1 , 2 1 f 2 = 2 2 = 4 1 4 = 4 2 , 3 1 f 3 = 3 2 = 9 1 9 = 9 3 , 4 1 f 4 = 4 2 = 16 1 16 = 16 c) To find: Draw and shade the approximating rectangles for the LRAM and to find the area. The approximating rectangles for the LRAM and the area is A ≈ 14 Given information: f x = x 2 in the interval 0 , 4 Calculation: For LRAM there is no rectangle in the interval 0.1 A ≈ 1 + 4 + 9 = 14 Subintervals Base Height Area 1 , 2 1 1 f 1 = 1 2 = 1 1 1 = 1 2 , 3 1 f 2 = 2 2 = 4 1 4 = 4 3 , 4 1 f 3 = 3 2 = 9 1 9 = 9 d) To find: Average area of RRAM and.LRAM. Average area of RRAM and.LRAM is 22 Given information: f x = x 2 in the interval 0 , 4 Calculation: Using RRAM the area is 30 and using LRAM the are is 14 the average estimate of the area is 30 + 14 2 = 22

PRECALCULUS:GRAPHICAL,...-NASTA ED.

PRECALCULUS:GRAPHICAL,...-NASTA ED.

10th Edition

ISBN: 9780134672090

Author: Demana

Publisher: PEARSON

See similar textbooks

Expert Solution & Answer

Chapter 11.2, Problem 17E

Solution

a)

To find: Draw the graph of the function for x in the specified interval and to verify that the function is non-negative in that interval.

The graph of the function $fx=x2$ in the interval $0,4$ is,

Given information:

$fx=x2$ in the interval $0,4$

Calculation:

Plotting the graph

b)

To find: Draw and shade the approximating rectangles for the RRAM and to find the area.

The approximating rectangles for the RRAM and the area is,

$A≈30$

Given information:

$fx=x2$ in the interval $0,4$

Calculation:

The four sub-intervals are $0,1,1,2,2,3,3,4$

For RRAM the upper right corners of the rectangles touch the graph of the function

Each rectangles has a base of 1 while the heights are function value at the right-hand endpoint.

$A≈1+4+9=14$

Subintervals Base Height Area
$0,1$ $1$ $f1=12=1$ $11=1$
$1,2$ $1$ $f2=22=4$ $14=4$
$2,3$ $1$ $f3=32=9$ $19=9$
$3,4$ $1$ $f4=42=16$ $116=16$

c)

To find: Draw and shade the approximating rectangles for the LRAM and to find the area.

The approximating rectangles for the LRAM and the area is

$A≈14$

Given information:

$fx=x2$ in the interval $0,4$

Calculation:

For LRAM there is no rectangle in the interval $0.1$

$A≈1+4+9=14$

Subintervals Base Height Area
$1,2$ $1$ $1$ $f1=12=1$ $11=1$
$2,3$ $1$ $f2=22=4$ $14=4$
$3,4$ $1$ $f3=32=9$ $19=9$

d)

To find: Average area of RRAM and.LRAM.

Average area of RRAM and.LRAM is $22$

Given information:

$fx=x2$ in the interval $0,4$

Calculation:

Using RRAM the area is $30$ and using LRAM the are is $14$ the average estimate of the area is

$30+142=22$

Chapter 11.2, Problem 16E

Chapter 11.2, Problem 18E

Chapter 11 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 11.1 - Prob. 1QR Ch. 11.1 - Prob. 2QR Ch. 11.1 - Prob. 3QR Ch. 11.1 - Prob. 4QR Ch. 11.1 - Prob. 5QR Ch. 11.1 - Prob. 6QR Ch. 11.1 - Prob. 7QR Ch. 11.1 - Prob. 8QR Ch. 11.1 - Prob. 9QR Ch. 11.1 - Prob. 10QR

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E Ch. 11.1 - Prob. 11E Ch. 11.1 - Prob. 12E Ch. 11.1 - Prob. 13E Ch. 11.1 - Prob. 14E Ch. 11.1 - Prob. 15E Ch. 11.1 - Prob. 16E Ch. 11.1 - Prob. 17E Ch. 11.1 - Prob. 18E Ch. 11.1 - Prob. 19E Ch. 11.1 - Prob. 20E Ch. 11.1 - Prob. 21E Ch. 11.1 - Prob. 22E Ch. 11.1 - Prob. 23E Ch. 11.1 - Prob. 24E Ch. 11.1 - Prob. 25E Ch. 11.1 - Prob. 26E Ch. 11.1 - Prob. 27E Ch. 11.1 - Prob. 28E Ch. 11.1 - Prob. 29E Ch. 11.1 - Prob. 30E Ch. 11.1 - Prob. 31E Ch. 11.1 - Prob. 32E Ch. 11.1 - Prob. 33E Ch. 11.1 - Prob. 34E Ch. 11.1 - Prob. 35E Ch. 11.1 - Prob. 36E Ch. 11.1 - Prob. 37E Ch. 11.1 - Prob. 38E Ch. 11.1 - Prob. 39E Ch. 11.1 - Prob. 40E Ch. 11.1 - Prob. 41E Ch. 11.1 - Prob. 42E Ch. 11.1 - Prob. 43E Ch. 11.1 - Prob. 44E Ch. 11.1 - Prob. 45E Ch. 11.1 - Prob. 46E Ch. 11.1 - Prob. 47E Ch. 11.1 - Prob. 48E Ch. 11.1 - Prob. 49E Ch. 11.1 - Prob. 50E Ch. 11.1 - Prob. 51E Ch. 11.1 - Prob. 52E Ch. 11.1 - Prob. 53E Ch. 11.1 - Prob. 54E Ch. 11.1 - Prob. 55E Ch. 11.1 - Prob. 56E Ch. 11.1 - Prob. 57E Ch. 11.2 - Prob. 1QR Ch. 11.2 - Prob. 2QR Ch. 11.2 - Prob. 3QR Ch. 11.2 - Prob. 4QR Ch. 11.2 - Prob. 5QR Ch. 11.2 - Prob. 6QR Ch. 11.2 - Prob. 7QR Ch. 11.2 - Prob. 8QR Ch. 11.2 - Prob. 9QR Ch. 11.2 - Prob. 10QR Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E Ch. 11.2 - Prob. 4E Ch. 11.2 - Prob. 5E Ch. 11.2 - Prob. 6E Ch. 11.2 - Prob. 7E Ch. 11.2 - Prob. 8E Ch. 11.2 - Prob. 9E Ch. 11.2 - Prob. 10E Ch. 11.2 - Prob. 11E Ch. 11.2 - Prob. 12E Ch. 11.2 - Prob. 13E Ch. 11.2 - Prob. 14E Ch. 11.2 - Prob. 15E Ch. 11.2 - Prob. 16E Ch. 11.2 - Prob. 17E Ch. 11.2 - Prob. 18E Ch. 11.2 - Prob. 19E Ch. 11.2 - Prob. 20E Ch. 11.2 - Prob. 21E Ch. 11.2 - Prob. 22E Ch. 11.2 - Prob. 23E Ch. 11.2 - Prob. 24E Ch. 11.2 - Prob. 25E Ch. 11.2 - Prob. 26E Ch. 11.2 - Prob. 27E Ch. 11.2 - Prob. 28E Ch. 11.2 - Prob. 29E Ch. 11.2 - Prob. 30E Ch. 11.2 - Prob. 31E Ch. 11.2 - Prob. 32E Ch. 11.2 - Prob. 33E Ch. 11.2 - Prob. 34E Ch. 11.2 - Prob. 35E Ch. 11.2 - Prob. 36E Ch. 11.2 - Prob. 37E Ch. 11.2 - Prob. 38E Ch. 11.2 - Prob. 39E Ch. 11.2 - Prob. 40E Ch. 11.2 - Prob. 41E Ch. 11.2 - Prob. 42E Ch. 11.2 - Prob. 43E Ch. 11.2 - Prob. 44E Ch. 11.2 - Prob. 45E Ch. 11.2 - Prob. 46E Ch. 11.2 - Prob. 47E Ch. 11.2 - Prob. 48E Ch. 11.2 - Prob. 49E Ch. 11.2 - Prob. 50E Ch. 11.2 - Prob. 51E Ch. 11.2 - Prob. 52E Ch. 11.2 - Prob. 53E Ch. 11.2 - Prob. 54E Ch. 11.2 - Prob. 55E Ch. 11.2 - Prob. 56E Ch. 11.2 - Prob. 58E Ch. 11.2 - Prob. 59E Ch. 11.2 - Prob. 60E Ch. 11.2 - Prob. 61E Ch. 11.2 - Prob. 62E Ch. 11.2 - Prob. 63E Ch. 11.2 - Prob. 64E Ch. 11.3 - Prob. 1QR Ch. 11.3 - Prob. 2QR Ch. 11.3 - Prob. 3QR Ch. 11.3 - Prob. 4QR Ch. 11.3 - Prob. 5QR Ch. 11.3 - Prob. 6QR Ch. 11.3 - Prob. 7QR Ch. 11.3 - Prob. 8QR Ch. 11.3 - Prob. 9QR Ch. 11.3 - Prob. 10QR Ch. 11.3 - Prob. 1E Ch. 11.3 - Prob. 2E Ch. 11.3 - Prob. 3E Ch. 11.3 - Prob. 4E Ch. 11.3 - Prob. 5E Ch. 11.3 - Prob. 6E Ch. 11.3 - Prob. 7E Ch. 11.3 - Prob. 8E Ch. 11.3 - Prob. 9E Ch. 11.3 - Prob. 10E Ch. 11.3 - Prob. 11E Ch. 11.3 - Prob. 12E Ch. 11.3 - Prob. 13E Ch. 11.3 - Prob. 14E Ch. 11.3 - Prob. 15E Ch. 11.3 - Prob. 16E Ch. 11.3 - Prob. 17E Ch. 11.3 - Prob. 18E Ch. 11.3 - Prob. 19E Ch. 11.3 - Prob. 20E Ch. 11.3 - Prob. 21E Ch. 11.3 - Prob. 22E Ch. 11.3 - Prob. 23E Ch. 11.3 - Prob. 24E Ch. 11.3 - Prob. 25E Ch. 11.3 - Prob. 26E Ch. 11.3 - Prob. 27E Ch. 11.3 - Prob. 28E Ch. 11.3 - Prob. 29E Ch. 11.3 - Prob. 30E Ch. 11.3 - Prob. 31E Ch. 11.3 - Prob. 32E Ch. 11.3 - Prob. 33E Ch. 11.3 - Prob. 34E Ch. 11.3 - Prob. 35E Ch. 11.3 - Prob. 36E Ch. 11.3 - Prob. 37E Ch. 11.3 - Prob. 38E Ch. 11.3 - Prob. 39E Ch. 11.3 - Prob. 40E Ch. 11.3 - Prob. 41E Ch. 11.3 - Prob. 42E Ch. 11.3 - Prob. 43E Ch. 11.3 - Prob. 44E Ch. 11.3 - Prob. 45E Ch. 11.3 - Prob. 46E Ch. 11.3 - Prob. 47E Ch. 11.3 - Prob. 48E Ch. 11.3 - Prob. 49E Ch. 11.3 - Prob. 50E Ch. 11.3 - Prob. 51E Ch. 11.3 - Prob. 52E Ch. 11.3 - Prob. 53E Ch. 11.3 - Prob. 54E Ch. 11.3 - Prob. 55E Ch. 11.3 - Prob. 56E Ch. 11.3 - Prob. 57E Ch. 11.3 - Prob. 58E Ch. 11.3 - Prob. 59E Ch. 11.3 - Prob. 60E Ch. 11.3 - Prob. 61E Ch. 11.3 - Prob. 62E Ch. 11.3 - Prob. 63E Ch. 11.3 - Prob. 64E Ch. 11.3 - Prob. 65E Ch. 11.3 - Prob. 66E Ch. 11.3 - Prob. 67E Ch. 11.3 - Prob. 68E Ch. 11.3 - Prob. 69E Ch. 11.3 - Prob. 70E Ch. 11.3 - Prob. 71E Ch. 11.3 - Prob. 72E Ch. 11.3 - Prob. 73E Ch. 11.3 - Prob. 74E Ch. 11.3 - Prob. 75E Ch. 11.3 - Prob. 76E Ch. 11.3 - Prob. 77E Ch. 11.3 - Prob. 78E Ch. 11.3 - Prob. 79E Ch. 11.3 - Prob. 80E Ch. 11.3 - Prob. 81E Ch. 11.3 - Prob. 82E Ch. 11.3 - Prob. 83E Ch. 11.3 - Prob. 84E Ch. 11.3 - Prob. 85E Ch. 11.3 - Prob. 86E Ch. 11.3 - Prob. 88E Ch. 11.3 - Prob. 89E Ch. 11.3 - Prob. 90E Ch. 11.3 - Prob. 91E Ch. 11.3 - Prob. 92E Ch. 11.3 - Prob. 93E Ch. 11.4 - Prob. 1QR Ch. 11.4 - Prob. 2QR Ch. 11.4 - Prob. 3QR Ch. 11.4 - Prob. 4QR Ch. 11.4 - Prob. 5QR Ch. 11.4 - Prob. 6QR Ch. 11.4 - Prob. 7QR Ch. 11.4 - Prob. 8QR Ch. 11.4 - Prob. 9QR Ch. 11.4 - Prob. 10QR Ch. 11.4 - Prob. 1E Ch. 11.4 - Prob. 2E Ch. 11.4 - Prob. 3E Ch. 11.4 - Prob. 4E Ch. 11.4 - Prob. 5E Ch. 11.4 - Prob. 6E Ch. 11.4 - Prob. 7E Ch. 11.4 - Prob. 8E Ch. 11.4 - Prob. 9E Ch. 11.4 - Prob. 10E Ch. 11.4 - Prob. 11E Ch. 11.4 - Prob. 12E Ch. 11.4 - Prob. 13E Ch. 11.4 - Prob. 14E Ch. 11.4 - Prob. 15E Ch. 11.4 - Prob. 16E Ch. 11.4 - Prob. 17E Ch. 11.4 - Prob. 18E Ch. 11.4 - Prob. 19E Ch. 11.4 - Prob. 20E Ch. 11.4 - Prob. 21E Ch. 11.4 - Prob. 22E Ch. 11.4 - Prob. 23E Ch. 11.4 - Prob. 24E Ch. 11.4 - Prob. 25E Ch. 11.4 - Prob. 26E Ch. 11.4 - Prob. 27E Ch. 11.4 - Prob. 28E Ch. 11.4 - Prob. 29E Ch. 11.4 - Prob. 30E Ch. 11.4 - Prob. 31E Ch. 11.4 - Prob. 32E Ch. 11.4 - Prob. 33E Ch. 11.4 - Prob. 34E Ch. 11.4 - Prob. 35E Ch. 11.4 - Prob. 36E Ch. 11.4 - Prob. 37E Ch. 11.4 - Prob. 38E Ch. 11.4 - Prob. 39E Ch. 11.4 - Prob. 40E Ch. 11.4 - Prob. 41E Ch. 11.4 - Prob. 42E Ch. 11.4 - Prob. 43E Ch. 11.4 - Prob. 44E Ch. 11.4 - Prob. 45E Ch. 11.4 - Prob. 46E Ch. 11.4 - Prob. 47E Ch. 11.4 - Prob. 48E Ch. 11.4 - Prob. 49E Ch. 11.4 - Prob. 51E Ch. 11.4 - Prob. 52E Ch. 11.4 - Prob. 54E Ch. 11.4 - Prob. 55E Ch. 11.4 - Prob. 56E Ch. 11.4 - Prob. 57E Ch. 11 - Prob. 1RE Ch. 11 - Prob. 2RE Ch. 11 - Prob. 3RE Ch. 11 - Prob. 4RE Ch. 11 - Prob. 5RE Ch. 11 - Prob. 6RE Ch. 11 - Prob. 7RE Ch. 11 - Prob. 8RE Ch. 11 - Prob. 9RE Ch. 11 - Prob. 10RE Ch. 11 - Prob. 11RE Ch. 11 - Prob. 12RE Ch. 11 - Prob. 13RE Ch. 11 - Prob. 14RE Ch. 11 - Prob. 15RE Ch. 11 - Prob. 16RE Ch. 11 - Prob. 17RE Ch. 11 - Prob. 18RE Ch. 11 - Prob. 19RE Ch. 11 - Prob. 20RE Ch. 11 - Prob. 21RE Ch. 11 - Prob. 22RE Ch. 11 - Prob. 23RE Ch. 11 - Prob. 24RE Ch. 11 - Prob. 25RE Ch. 11 - Prob. 26RE Ch. 11 - Prob. 27RE Ch. 11 - Prob. 28RE Ch. 11 - Prob. 29RE Ch. 11 - Prob. 30RE Ch. 11 - Prob. 31RE Ch. 11 - Prob. 32RE Ch. 11 - Prob. 33RE Ch. 11 - Prob. 34RE Ch. 11 - Prob. 35RE Ch. 11 - Prob. 36RE Ch. 11 - Prob. 37RE Ch. 11 - Prob. 38RE Ch. 11 - Prob. 40RE

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