Use the three functions shown. 1. f(x)=x² II. f(x)=√x III. f(x) = ln x For which of the functions, if any, is a trapezoidal approximation for the area under the curve y = f(x) over the interval [1, 4] with 3 equal subintervals less than the midpoint approximation? none of the functions O I only II and III only all of the functions​

Use The Three Functions Shown. 1. F(x)=x II. F(x)=x III. F(x) = Ln X For Which Of The Functions, If Any,

Answers

Answer 1

II and III only

We split up the integration interval [1, 4] into 3 equally-spaced subintervals of length (4 - 1)/3 = 1 :

[1, 2], [2, 3], [3, 4]

The area over each subinterval [L, R] is either approximated by a trapezoid, whose area will be

1 • (f(L) + f(R))/2

or by a rectangle with height f((L + R)/2) and hence area

1 • f((L + R)/2)

For f(x) = x², the area under f(x) over [1, 4] is approximated by

• using trapezoids (T) :

[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}{2\times3} (1^2 + 2\times2^2 + 2\times3^2 + 4^2) = \frac{43}2 = \frac{86}4[/tex]

• using midpoints (M) :

[tex]\displaystyle \int_1^4 x^2 \, dx \approx \frac{4-1}3 \left(\left(\frac32\right)^2 + \left(\frac52\right)^2 + \left(\frac72\right)^2\right) = \frac{83}4[/tex]

so T > M. (This eliminates "I only" and "all of the functions".)

For f(x) = √x, the area is approximated by

• T :

[tex]\displaystyle \int_1^4 \sqrt x \, dx \approx \frac{4-1}{2\times3} (\sqrt1 + 2\sqrt2 + 2\sqrt3 + \sqrt4) \approx 4.646[/tex]

• M :

[tex]\displaystyle \int_1^4 \sqrt x\, dx \approx \frac{4-1}3 \left(\sqrt{\frac32} + \sqrt{\frac52} + \sqrt{\frac72}\right) \approx 4.677[/tex]

so T < M. (This eliminates "none of the functions".)


Related Questions

0/10 5/10 10/10 or a 1
Decimals:0.0 0.5 1.0. Write the fraction OR mixed number and the "Decimals" show by the model. Explain.​

Answers

Answer:

1/2

Step-by-step explanation:

: 0.5 as a fraction is written as 1/2

 HELP
Dieing from math in the picture. I think I did it wrong. Please help. :(

Answers

X = 352.3 [your work is correct]

then the perimeter would be 352.3 + 352.3 + 280 + 280 = 1,264.55

Please PLEASE HELP someone explain how the answer is 0.3112

Answers

You first have to add the total number of pedestrian deaths

[tex]52+252+86+587=977[/tex]

You then have to find the number of civilians that were intoxicated when they died

[tex]52+252=304[/tex]

Divide that number by the total number of pedestrian deaths

[tex]=304/977\\\\=0.3111566018\\\\=0.3112[/tex]

What is the shortest strip of fiber from which five pieces of the following lengths can be cut: 9 1/2 inches, 10 11/16 inches, 6 9/16 inches, 7 1/2 inches, and 1 5/8 inches? No allowance is made for waste.​

Answers

Answer:

35 7/8 inches

Step-by-step explanation:

Shortest strip

9 1/2 + 10 11/16 + 6 9/16 + 7 1/2 + 1 5/89 8/16 + 10 11/16 + 6 9/16 + 7 8/16 + 1 10/169 + 10 + 6 + 7 + 1 + (46/16)33 + 2 7/835 7/8 inches

Three line segments have measures of 18, 12, and 10 Will the segments form a triangle?

Answers

Answer:

Yes, the given segments will form a triangle

Step-by-step explanation:

Condition: If sum of the measures of any two segments of a triangle is greater than the third segment, then they will form a triangle.

Lengths of the given segments are 18, 12 and 10 units.18 + 12 = 30 > 1012 + 10 = 22 > 1810 + 18 = 28 > 12

Here, lengths of the given segments obey the above mentioned condition. So, they will form a triangle.

state whether each is a property that shows congruence between two triangles using Yes or No.

_____ 2. SSS
_____ 5. SAS
_____ 3. SSA
_____ 6. ASA
_____ 4. AAS
_____ 7. AAA

Answers

Answer:

yes

yes

no

yes

yes

no

Step-by-step explanation:

. What is (f + g)(x)?
=
-
f(x) = x3 - 2x + 3
g(x) = 2x² + 4x - 4
-

Answers

Answer:

[tex]3x^3 + 2x - 1[/tex]

Step-by-step explanation:

[tex]x^3 - 2x + 3 + 2x^3 + 4x - 4[/tex]

Combine like terms:

[tex]3x^3 + 2x - 1[/tex]

Hope that helped

(f+g)(x)f(x)+g(x)x³-2x+3+2x³+4x-4x³+2x³-2x+4x+3-43x³+2x-1

Juan played 2 hours of video games per day. How many hours does he play in 6 days

Answers

He would play 12 hours

Explanation: 2 hours every day would just be 2 x 6 which equals 12

Answer:

12 hours

Step-by-step explanation:

you take the amount of hours and multiple it by the days. so 2x6=12

Simplify y ^2 + 11y - 6y + y ^2.
y4 + 5 y
2 y 2 + 5 y
y4 + 5
2 y 2 + 5

Answers

Step-by-step explanation:

Question:

[tex] {y}^{2} + 11y - 6y + {y}^{2} [/tex]

Organize the like terms...

[tex] = {y}^{2} + {y}^{2} + 11y - 6y[/tex]

[tex] = 2 {y}^{2} + 5y[/tex]

Answer:

2y^2 + 5y

Step-by-step explanation:

y^2 + 11y - 6y + y^2=

= (y^2 + y^2) + (11y - 6y)

= 2y^2 + 5y

Which graft represent -3x+5y=-15

Answers

The graph of the function -3x+5y=-15 is a linear function we can draw it by finding the values of y for every value of x.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

-3x + 5y = -15

The above function shows a linear function we can write it as:

5y = 3x - 15

y = (3x - 15)/5

If x = 0, y = -3

x = 1, y = -2.4

x = 2, y = -1.8

x = -1, y = -3.6

x = -2, y = -4.2

Thus, the graph of the function -3x+5y=-15 is a linear function we can draw it by finding the values of y for every value of x.

Learn more about the function here:

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Multiply and simplify (4x-2)(3x^2-2x+1) Write answer in standard form

Answers

Answer:

12x^3 - 14x^2 + 8x - 2

Answer:

12[tex]x^{3}[/tex] - 14x² + 8x - 2

Step-by-step explanation:

1. Distribute the parentheses:

4x(3x²) + 4x(-2x) + 4x(1) + (-2)(3x²) + (-2)(-2x) + (-2)(1)

2. Multiply:

12[tex]x^{3}[/tex] + (-8x²) + 4x + -6x² + 4x + (-2)

3. Combine like terms:

12[tex]x^{3}[/tex] - 14x² + 8x -2

hope this helps!

Tidal energy is powered by:
A. Earth's gravity.
B. the moon's gravity.
C. the thermocline of the ocean.

Answers

Tidal energy is powered by the moon's gravity

COS(60°) what is the answer

Answers

Answer:

1/2

Step-by-step explanation:

10 in.
12 in.
8 in.
Find the surface area

Answers

Answer:

592 square inches

Step-by-step explanation:

2(S1)+2(S2)+2(S3)=SA

2(10*12)+2(12*8)+2(10*8)=SA

2(120)+2(96)+2(80)=SA

240+192+160=SA

SA=592 in. Squared

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Answers

the answer is 41 , this is because the angles have to add up to 180 in total therefore 180-139 = 41

Answer:

41

Step-by-step explanation:

Supplementary Angles add up to 180.

180 - 139 = 41

Simplify be using distributive property: 3(4x -3) + 5(2x - 1)

Answers

Answer:

25

Step-by-step explanation:

solve the inequality 23 + d > 35.

Answers

Answer:

[tex]d > 12[/tex]

Step-by-step explanation:

[tex]23+d > 35[/tex]
[tex]d > 12[/tex] (subtract 23 on both sides)

Use inverse operations to solve.
1. You had $37 in your bank account. After you receive some money for your birthday, you have a total of $62.
How much money did you get for your birthday?

Answers

Answer:

[tex]\huge\boxed{\bf\:25 \:dollars}[/tex]

Step-by-step explanation:

Money in the bank account before receiving the birthday money = $37

Money in the bank account after receiving the birthday money = $62

Money received as the birthday money = ?

Money received as the birthday money

= Money in the bank account after receiving the birthday money  - Money in the bank account before receiving the birthday money

= $62 - $37

= $25

[tex]\rule{150pt}{2pt}[/tex]

Phoebe divided her rectangular vegetable garden into three sections, as shown in the drawing below.

Answers

Photosynthesis is a process used by plants and other organisms to convert light energy into chemical energy that, through cellular respiration, can later be released to fuel the organism's activities

Tony made 52 decorations for the class party. He made 7 times as many ecorations as Jack did, but he lost 4. Which equation could be used to Find the number of decorations, x, Jack made?

⚫️4x + 7 = 52
⚫️7x + 4 = 52
⚫️4x - 7 = 52
⚫️7x - 4 = 52

Answers

7x-4=52 is correct because he made 7 times more than Jack which is 7x. For example if Jack made 8 decorations, 7 x (8) = 56. If you subtract 4 from 56 you get 52. Therefore, the equation 7x-4=52 is correct.
7x- 4 = 52 is the correct answer.

what is this qouschin

Answers

Answer:

Below in bold.

Step-by-step explanation:

m < 3 = 59 degrees (alternate angles)

m < 2 = 180 - 59 = 121 degrees  ( adjacent angles)

Write an equation to represent the following statement. 51 5151 divided by 3 33 is k kk.

Answers

The equation is a quotient statement, and the equation is 51/3 = k

How to determine the equation?

The statement is given as:

51 divided by 3 is k

Represent the word "is" with "="

So, we have:

51 divided by 3 = k

Represent the word "divided" with "/"

So, we have:

51 / 3 = k

Hence, the equation is 51/3 = k

Read more about equations at:

https://brainly.com/question/2972832

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Hello, we need help with these questions

Answers

Answer:

...

Step-by-step explanation:

Reggie put $400 in a savings account that earns 6% interest each year how much money will he have in his account after two years??

Answers

Answer:

Your answer is 4800

Step-by-step explanation:

I: PRT

400

  .6

____

2400

0000

_____

2400

       2

_____

4800

Have a wonderful day/night and good luck

stay safe, and stay healthy

Ty for brainliest!

Answer:

4800

Step-by-step explanation:

Alex buys 24 apples from the supermarket. When he gets home, he finds that 6 apples are bad. What percentage of the apples are bad? Round your answer to the nearest number.

Answers

Answer:

25%

Step-by-step explanation:

6/24 of the apples went bad

we can still simplify 6/24

1/4

1/4 is equal to 25%

hope this helps

you won 1 million dollars in prize money, however they are not giving it to you all at once. so is your money trult the value of the prize

Answers

I guess it’s going to be 1million + 2miilion )

Two sailboats leave Key Largo, Florida. One of the sailboats travels 3 miles east and then 4 miles north. The second sailboat travels 8 miles south and 6 miles west. How far apart, in miles, are the boats? A. 14 miles B. 15 miles C. 17 miles D. 21 miles​

Answers

Check the picture below.

Jacob earns $60 in 2 hours , or $150 in 5 hours. Write and equation to represent his earnings.

Answers

Answer:

2      

Step-by-step explanation:

if you divided each number by the minute time you would then divide both numbers like 2 x 60 + 60 and 5 x 60+60+60+60+60=300 divided that with the two numbers and then you get 2

write the ratio in simplest form 24:4

Answers

Answer:

6:1

Formula for this equation

Divide by 4

24 ÷ 4 = 6

4 ÷ 4 = 1

The correct answer to ratio is 6:1

Can you guys help me please :(

Answers

The area of the first, second, third, and fourth circles will be 56.72 cm², 36.3 ft², 167.33 m², and 188.6 yd² respectively.

What is a circle?

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

Then the radius and diameter are given below.

[tex]\rm r_1 = 4 \dfrac{1}{4} = \dfrac{17}{4} = 4.25 \ cm\\\\\\r_2 = \dfrac{d}{2} = \dfrac{6\frac{4}{5}}{2} = \dfrac{34}{10} = 3.4 \ ft\\\\\\r_3 = \dfrac{d}{2} = \dfrac{14.6}{2} = 7.3 \ m\\\\\\r_4 = 7\dfrac{3}{4} = \dfrac{31}{4} = 7.75 \ yd[/tex]

Then the area of the circle is given as

Area = π × r²

Then the area of the first circle will be

Area = π × r₁²

Area = 3.14 × 4.25²

Area = 56.72 square cm

Then the area of the second circle will be

Area = π × r₂²

Area = 3.14 × 3.4²

Area = 36.3 square ft

Then the area of the third circle will be

Area = π × r₃²

Area = 3.14 × 7.3²

Area = 167.33 square m

Then the area of the fourth circle will be

Area = π × r₁²

Area = 3.14 × 7.75²

Area = 188.6 square yd

More about the circle link is given below.

https://brainly.com/question/11833983

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