Mathematics High School

Express the limit as a definite integral on the given interval.
n lim Σ [4(xi*)3 − 7xi*]Δx, [2, 5]
n→[infinity] i = 1 ∫ ( ________ ) dx
2

Answers

Answer 1

The given limit can be expressed as a definite integral on the interval [2, 5] by using the definition of a Riemann sum:

lim Σ [4(xi*)3 − 7xi*]Δx, [2, 5]
n→[infinity] i = 1

This can be rewritten as:

lim Σ [(4(xi*)3 − 7xi*)/2] 2(n/2)Δx, [2, 5]
n→[infinity] i = 1

where Δx = (5 - 2)/n = 3/n and xi* is any point in the ith subinterval [xi-1, xi]. We have also divided n into 2 equal parts to get 2(n/2)Δx.

Now, we can express the above Riemann sum as a definite integral by taking the limit of the sum as n approaches infinity:

lim n→[infinity] Σ [(4(xi*)3 − 7xi*)/2] 2(n/2)Δx

= lim n→[infinity] Σ [(4(xi*)3 − 7xi*)/2] (5-2)/n (n/2)

= lim n→[infinity] Σ [(4(xi*)3 − 7xi*)/2] (3/2)

= ∫2^5 [(4x^3 − 7x)/2] dx

Therefore, the limit can be expressed as the definite integral:

∫2^5 [(4x^3 − 7x)/2] dx.

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Related Questions


Use properties of operations to determine whether or not the expressions (x + 10) + x + 9 and 2(x + 7) + 5 are
equivalent

Answers

Answer:

The expressions are equivalent.

Step-by-step explanation:

We can simplify each expression and compare the results.

(x + 10) + x + 9 = x + 10 + x + 9 = 2x + 19

2(x + 7) + 5 = 2x + 14 + 5 = 2x + 19

2x + 19 = 2x + 19

Answer: The expressions are equivalent.

Enter the value of 2 (4x + 3) when x = 3.

Answers

Answer:

30 is your answer

Step-by-step explanation:

2(12+3)

=30

30, 4x3=12, 12+3=15, 15x2=30

Which perfect squares does the number 73 falls in between?

Answers

Answer:

64 and 81

Step-by-step explanation:

8×8=64 and 9×9=81. 73 falls between these two numbers.

Which is greater 2.6 or 2.65 ?

Answers

Answer:

2.65 is greater than 2.6

Step-by-step explanation:

if 65 is greater than 60 than 2.65 is greater than 2.60

Answer:

2.6 > 2.65

Step-by-step explanation:

Find the missing side of the triangle. Round to the nearest tenth.
A) 5.5
C) 14.1
B) 12.7
D) 9.5

Answers

5.5 because In front of a 30 degree angle is a cathete of half of Hypotenuse.

What fraction is less than 1/2. 3/4,1/6,6/12,4/10,5/8,5/2

Answers

1/6! Any fraction that represents less than a half of a whole is less than 1/2. You could also convert them to the same denominator and see the difference. Make sure whatever you do to the first fraction, you do to the other!

Answer:

1/6 and 4/10

Step-by-step explanation:

1/2 = 0.5 and 0.5 is greater than 1/6 which is 0.166666666667 and 4/10 which is 0.4.

I NEED HELP PLZ HELP ME

Answers

Answer:

a) 50+10p

b) 30+12p

c) 10 pies

d) $150

Step-by-step explanation:

The answer to this question is B

Adult tickets to a play cost $22 tickets for kids cost $15. Tickets for a group of 11 cost a total of $228. How many children and how many adults went to the play?

Answers

Answer:Number of children = 2 and number of adults = 9 attended the play

Step-by-step explanation:

Step 1

Let the  number  of children be represented as  x

and the number of adults in the group  be represented as  as y

such that the total number of the group that went to the play

= x+y=11--- equation 1

And the total cost paid for the play will be expressed as

15x+  22y= 228------ equation 2

Step 2-- Solving

x+y=11--- equation 1

15x+  22y= 228------ equation 2

B y elimination method, multiply equation 1 by 15 to give equation 3  and then subtract from equation 2

15x+  22y= 228------ equation 2

15x+15Y= 165----- equation 3

7y=63

y= 63/7= 9

y= adults = 9

therefore x = number of children will be

x+y=11

x+ 9=11

x= 11-9= 2

In the group that attended the play,  Number of children = 2 and number of adults = 9

An octagonal prism has...........lateral faces.
8
2
7
5

Answers

Answer:

an octagonal prism has 8 lateral faces

Answer:

8

Step-by-step explanation:

An octagonal prism has 8 lateral faces.

An octagonal prism has 10 faces – 8 lateral faces and 2 bases, 16 vertices, and 24 edges

Write an equation of the line that passes through (2, 1) and is parallel to the line y=2x+7.

Answers

Answer: y=2x-3

Step-by-step explanation:

Use the figure to find the measures of the numbered angles. ∠3 = ∘ ∠4 = ∘

Answers

Answer:

Step-by-step explanation:

∠3=95 (corresponding angle)

∠4=180-95

    =85

Which set of ordered pairs is linear? A. {(2, 1), (5, 1), (6, 1)} B. {(–1, 4), (0, 0), (1, 6)} C. {(–3, 5), (1, 0), (2, 4)} D. {(0, 0), (1, 3), (2, 7)}

Answers

Answer:

merhaba ben yeni geledimde adın ne

please help me with this problem

Answers

Answer:

vitamin c is the independent variable

Step-by-step explanation:

the amount of vitaman c dose not change but the amount of oranges eaten can change

Can someone help me with these 2 problems thank you

Answers

Answer:

For question 6 there are 3 steps, and for question 7 there are 2 steps

Step-by-step explanation:

Question 6:

step 1. 89 x 2=178

step 2. 89 x 3=267

step 3. 267 + 178=445

Question 7:

step 1. 35 x 3= 105

step 2. 25 x 5= 12

Your're welcome :)

Select the correct answer.
The surface area (SA) of a cube with a as the length of each of its sides is given by the formula SA = 6a2. If the surface area is known, how can
you rewrite the formula to find its side?
ОА va
OB. VSA
OC a = $
OD. =

Answers

Answer:

(A). [tex]\sqrt{\frac{SA}{6} }[/tex]

Step-by-step explanation:

Round to the nearest tenth.

x=

y=

Answers

I could be wrong but I’m pretty sure x≈102.2 and y≈58

what sin40? round to the nearest hundredth place

Answers

Answer:

i don't know  just ask the internet

Answer:

0.75

Step-by-step explanation:

original answer: 0.74511316047

41,692.58

Which number is in the tenths place?
A. 2
B. 5
C. 8
D. 9

Answers

5 hope that helped :)

Answer:

5 is in the tenths place

Step-by-step explanation:

2 is in the ones place, 8 is in the hundredths place, and 9 is in the tens place.

what is the answer for 2x=7

Answers

Answer:

x=3.5

the answer is 3.5 because 7 divided by 2 is 3.5

if anyone is able to help please do :)

Answers

Answer:

49.12?

Step-by-step explanation:

half circle= 4 squared *3.14/2=25.12

triangle=pythagorean theorem to find h=8. 8*6/2= 24

25.12+24=49.12

An ice cream company fills containers with 64 ounces of ice cream. The acceptable percentage of error in filling each
ice cream container is 1.5%.
Select all the expressions that could be used to find the greatest number of ounces of ice cream each container can
hold.
64(1.15)
64(1.015)
64(1.5)+64
64-64(1.5)
64(0.015)-64
64+64(0.015)

Answers

Answer:

64(1.015)64+64(0.015)

Step-by-step explanation:

The target number is 64 and the error is 1.5%

Possible number is

64 ± 1.5% of 64 = 64 ± 0.015*64

The top limit is:

64 + 64(0.015) or64*(1.015)

Correct choices are B and F

64(1.015)

and

64+64(0.015)

PLEASE PLEASE, ANSWER ASAP
​

Answers

Answer: 16

Step-by-step explanation: 16 is how much the breaking pad is produced per hour because if you divide all of them you get 16 for each of them on the table

in the product rule for exponents, what do you do to the coefficients? what do you do to the exponents?

Answers

Answer:

Do not multiply the coefficients and the exponents. Remember, using the Product Rule add the exponents when the bases are the same.

In the product rule of the exponents,

''For same base we can add the exponents of the coefficients.''

What is mean by expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

Solve expression by using the product rule for exponents.

Now, We know that;

In the product rule for exponents;

When expression have same base then its exponents are add and the coefficients of expression are written as same as write in expression

Hence, In the product rule of the exponents,

''For same base we can add the exponents of the coefficients.''

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Neil has 2 pounds of grapes. He uses some to make a fruit salad. Now Neil has 8 ounces of grapes. How many ounces of grapes does Neil use for the fruit salad?

Answers

Answer:

Neil uses 24 ounces of grapes for the fruit salad.

Step-by-step explanation:

Quantity of grapes = 2 pounds

Use 1 pound = 16 ounces

So,

Quantity of grapes = 2(16) = 32 ounces

Neil uses some grapes to make a fruit salad. Now Neil has 8 ounces of grapes.

Quantity of grapes that Neil use for the fruit salad = [tex]32-8=24[/tex] ounces

Therefore,

Neil uses 24 ounces of grapes for the fruit salad.

35= h(b1+b2) solve for b2

Answers

Answer: look at the picture and I don’t know how to solve for b but I can do h

Step-by-step explanation: hope this help :)

Answer:

i dont know

Step-by-step explanation:

i dont know

If r = .15, this indicates

Answers

Answer:

Then D=.30

Step-by-step explanation:

Diameter is two times the radius

I think this is correct I'm not to sure

hope this helps :)

Put the following equation of a line into slope-intercept form, simplifying all
fractions.
2x - y = 4

Answers

Answer:

مرحبًا ، سأكون سعيدًا لمساعدتك في حبك في العمل ، وأريد المزيد من التفاصيل ، وسأبذل قصارى جهدي لإرضائك

Step-by-step explanation:

on squared paper draw the triangle with vertices at (1,1) , (5,3) , (3,5). find the area of the triangle​

Answers

Answer:

lol

Step-by-step explanation:

j

The area of the triangle is 6.

Will give Brainly! Please help!

Answers

Answer:

The answer is option c.

Hope this helps!

Please answer this question

Answers

y=3x-3

y=mx+b
m: slope, the line goes up 3 and over 1 so the slope is 3/1 which is 3
b: y intercept, the line crosses the y axis at -3 so b is -3
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