Which of the following is an improper integral?
A) the integral from 0 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
B) the integral from 1 to 3 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
C) the integral from negative 1 to 0 of the quotient of the quantity x plus 1 and the quantity 3 times x minus 2 dx
D) None of these

Answers

Answer 1

Answer:

A)  [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]

General Formulas and Concepts:

Calculus

Discontinuities

Removable (Hole) Jump Infinite (Asymptote)

Integration

IntegralsDefinite IntegralsIntegration Constant CImproper Integrals

Step-by-step explanation:

Let's define our answer choices:

A)  [tex]\displaystyle \int\limits^3_0 {\frac{x + 1}{3x - 2}} \, dx[/tex]

B)  [tex]\displaystyle \int\limits^3_1 {\frac{x + 1}{3x - 2}} \, dx[/tex]

C)  [tex]\displaystyle \int\limits^0_{-1} {\frac{x + 1}{3x - 2}} \, dx[/tex]

D) None of these

We can see that we would have a infinite discontinuity if x = 2/3, as it would make the denominator 0 and we cannot divide by 0. Therefore, any interval that includes the value 2/3 would have to be rewritten and evaluated as an improper integral.

Of all the answer choices, we can see that A's bounds of integration (interval) includes x = 2/3.

∴ our answer is A.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit:  Integration

Book: College Calculus 10e


Related Questions

Need help please asap

Answers

Answer:

A

Step-by-step explanation:

A because 21 is a greater number than 9 and therefore should be in the denominator. That leaves you with 9 which is a smaller number and should go on the numerator. Hope this helped you!

The marks of Riju in Mathematics test increased from 20 to 30. What is the percentage of increase?

Answers

Step-by-step explanation:

❀[tex] \underline{ \underline{ \text{Given}}} : [/tex]

Initial marks of Riju = 20Final marks of Riju = 30

Then, Increment of the marks = 30 - 20 = 10

❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

Percentage of increment

❀ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]

[tex] \boxed{ \sf{Percentage \: of \: increment = \frac{Increase \: of \: marks}{Initial \: marks} \times 100\%}}[/tex]

⇒ [tex] \sf{ \frac{10}{20} \times 100\%}[/tex]

⇒ [tex] \boxed{ \sf{50 \: \%}}[/tex]

[tex] \pink{ \boxed{ \boxed{ \bold{ \tt{Our \: final \: answer : \boxed{ \underline{ \tt{50\%}}}}}}}}[/tex]

Hope I helped ! ツ

Have a wonderful day / night ! ♡

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Name two planes that intersect in SW in the
figure to the right

Answers

Plane XTS and Plane VRS

A option

Need help with math homework

Answers

what is the question you need to ask

PLS help me
if you get it right i will give brainliest

Answers

Answer:

7.21

Step-by-step explanation:

Solution,

Given,

base = 4

perpendicular = 6

hypotenuse = ?

Now,

By the formula of Pythagoras Theorem,

h^2 = p^2 + b^2

h^2 = 6^2+4^2

h^2 = 36+16

h = sqrt ( 52 )

h = 7.21

Therefore, the value of x (hypotenuse) is 7.21 .

Answer:

x= 7.21///no

Step-by-step explanation:

4^2 + 6^2 = 52

take the square root which equals 7.21

///

Pythagorean triples consist of perfect squares, like 2^2 is for the side that is equal to 4, 6 is not a perfect square.

1 Which point has coordinates (2, 2)?

A. Point A
B. Point C
C. Point F
D. Point G


I NEED THIS NOW PLEASE HELP​

Answers

Answer:

g

Step-by-step explanation:

It’s answer D. Point G

Evaluate 1/2t + 3/8 when t = 1/4

Answers

Answer:

the answer is seven - eighths i think

Step-by-step explanation:

Answer

1/2

Evaluate: Enter a number for each variable.

1/2t+3/8

Evaluate for t=1/4

1/2 (1/4)+3/8

1/2 (1/4)+3/8

=1/2 or (Decimal: 0.5)

A pre-election survey showed that 3 out of every 5 citizens would vote in an election. At this rate, how many people would be expected to vote if there are 16,000 citizens in a city? 2,600 people

Answers

Answer:

9600 people would vote.

Step-by-step explanation:

3/5 = .6

16,000 * .6 = 9600

=
Solving a word problem with two unknowns using a linear...
A washer and a dryer cost $801 combined. The washer costs $51 more than the dryer. What is the cost of the dryer?

Answers

801 = x + 51 + x
801 = 2x + 51
750 = 2x
750/ 2 = 375
The dryer costs $375
375 + 51 = 426 ( washer costs )

Simplify (4/5)^-2. Show your work!
PLEASE HELP ASAP! 40 POINTS!

Answers

Answer: (16/25)

Step-by-step explanation: That's -(4/5) x -(4/5) = (16/25). It's that answer because a negative times a negative equals a positive. The exponent in the problem is telling you to multiply -4/5 times itself 2 times.

Write an equation of the line with the given slope and y-intercept. slope: -3 y-intercept: -6​

Answers

Answer:

The equation of line with  slope: -3 and y-intercept: -6​ is [tex]\mathbf{y=-3x-6}[/tex]

Step-by-step explanation:

We need to write an equation of the line with the given slope and y-intercept. slope: -3 ,y-intercept: -6​

The general equation for slope-intercept form is: [tex]y=mx+b[/tex]

where m is slope and b is y-intercept.

We are given in the question:

slope: -3 y-intercept: -6​

So, we have slope m = -3 and y-intercept b = -6

Putting values in the slope-intercept form equation:

[tex]y=mx+b\\y=-3x-6[/tex]

So, The equation of line with  slope: -3 and y-intercept: -6​ is [tex]\mathbf{y=-3x-6}[/tex]

A right rectangular prism has edge lengths of 1 1/3 inches, 2 inches, and 1 2/3 inches. What is the volume of the prism?

Answers

Answer:

264/9 = 29.34

Step-by-step explanation:

(11/3)*(12/3)*2

Answer:

29.34

Step-by-step explanation:

Find the missing lengths. Leave answer in simplest radical form.

Answers

a = 3

b= 3(root 2)

make sure to write the radical over the 2. i attached a picture of what it should look like

PLS HELP AND EXPLAINNN
Find the area of a circle with a radius of 9

i know the formula but im doing something wrong i need help

Answers

Answer:

A≈254 cm^2

Step-by-step explanation:

The area of a circle is given by formula:  π r^2

π  has a constant value of  3.14  And the radius of the circle is  9 c m

the area= π r^2 = 3.14 x (9)^2 cm^2

= 3.14 × ( 81 )

= 254.34 c m^2

≈ 254 c m^2

Can someone Help me with this ? :C and put in the Workings

Calculate the following by long or short division. Give your answers to TWO decimal places.

1.
[tex]456 \div 2[/tex]

2
[tex]538 \div 7[/tex]

Answers

Answer:  1. [tex]456\div2 =228[/tex] 2. [tex]538\div7=76.85[/tex]

Step-by-step explanation:

The given division problems :

[tex]1.\ 456\div2[/tex]

[tex]2.\ 538\div7[/tex]

By long division (see the attachment)

1. Divisor= 2

Dividend =456

Quotient = 228

Remainder =0

So, [tex]456\div2 =228[/tex]

2. Divisor= 7

Dividend = 538

Quotient =76.85

so, [tex]538\div7=76.85[/tex]

Clint completly filled his 18 gallon tank of gas with regular fuel for 55.08. As he left the gas station he noticed the station arcross the street sold regular fuel for 2. 99 Per gallon how much money could have clint saved per gallon is he had gone to the station across the street

Answers

Answer: 1.26

Step-by-step explanation:

Since he bought a 18 gallon tank of gas with regular fuel for 55.08.

The station across the street sold regular fuel for 2.99 per gallon. A 18 gallon tank will cost:

= 18 × 2.99

= 53.82

The amount that could have been saved would be:

= 55.08 - 53.82

= 1.26

Which set of expressions below does NOT represent equivalent expressions?

A. 8(3x + 7) and 8(3x) + 8(7)
B. 3(8x + 7) and 11x + 10
C. 7(3x + 8) and 7 ∙ 3x + 7∙ 8
D. 3(7x + 8) and 21x + 24

Answers

Answer:

B

Step-by-step explanation:

The other are equal

If a rectangle has a perimeter of 58 ft and a length of 4 feet what is the width of the rectangle?

Answers

Answer:

25ft

Hoped this helped!

Six segments form two triangles. AB = 3 cm, FE =11cm, CB = 9 cm, DE = 9 cm, CA=11 cm, and FD = 3 cm. (a) Write a triangle congruency statement. (b) What postulate guarantees that these triangles are congruent?​

Answers

That’s is 8cm if u want a


Step-by-step explanation

How many of the 100 bin A items can be recycled at a specialized center?

Answers

Depending on how big the center is, I would say 15.
I hope this helped!

taryn sold gift wrapping paper for a school project she sold 15 rolls of paper write an inequality to represent the amount she earned for the fundraiser

Answers

Answer:

Step-by-step explanation:

15× 8 = 120

Answer:

d ≥ 120

Step-by-step explanation:

Multiply 15 x 8

= 120

At Least means we use the ≥ sign.

So its d ≥ 120

Sorry if this is late!

i need help, it's due in a few minss plsssss​

Answers

Answer:3x^2*10x=30x^3

Step-by-step explanation:

[tex](\frac{1}{4} m^{2} n)^{3} * (-32m^{2}n)[/tex]

PLEASE PROVIDE AN EXPLANATION, I'M UNSURE OF HOW TO FIND THE ANSWER

Answers

Answer:

               [tex]\bold{(\frac14m^2n)^3*(-32m^2n)=-\frac12m^8n^4}[/tex]

Step-by-step explanation:

                                [tex](\frac14m^2n)^3*(-32m^2n)=\\\\=(\frac14)^3*(m^2)^3*n^3*(-32)*m^2*n=\\\\= \frac1{64}*m^{2\cdot3}*n^3*(-32)*m^2*n=\\\\= \frac1{64}*(-32)*m^{6}*m^2*n^3*n=\\\\=-\frac{32}{64}*m^{6+2}*n^{3+1}=\\\\=-\frac12m^8n^4[/tex]

Does this graph have 10 or 9 squares, 10 or 9 years, I think I might be going insane

Answers

Answer:

10 years

Step-by-step explanation:

I will give BRAINLIEST!!! Please answer as soon as possible

Answers

Answer:

2 c ( 7c + 1 )

Step-by-step explanation:

because 14 and 2 go into the table of 2

you first find out what number in table 2 go into 14 in this case 7 times 2 and then you find what number in the time table 2 give you 2 so it's 2 times 1. because it's c squared you can't not put both c inside due that would not be factorizing due that it's common and it does not have to be common.

so the answer will be 2c(7c+1)

online sales result in 35% of sales being returned to their local brick-and-mortar store. what is 35% of 2,000 purchases?

a. 70
b. 240
c. 350
d. 700

Answers

Answer:

b

Step-by-step explanation:

b

Answer:

D) 700

Step-by-step explanation:

I used a calculator so sorry if I can't give a explanation

5. (0,0) and (-2,-8) Slope=_ Equation=_​

Answers

You’re slope would be 4. And you’re slope equation would be y=4x

Factor f(x) 3x^3-4x^2-28x-16 given that (x+2) is a factor

Answers

Step-by-step explanation:

3x³ - 4x² - 28x - 16

= (x + 2)(Ax² + Bx + C)

= Ax³ + (2A + B)x² + (2B + C)x + 2C.

By Comparing Coefficients, we have:

A = 3,2A + B = -4,2B + C = -28,2C = -16.

Solving them will give A = 3, B = -10 and C = -8.

Hence 3x³ - 4x² - 28x - 16

= (x + 2)(3x² - 10x - 8)

= (x + 2)(3x + 2)(x - 4).

The answer is f(x) = (x + 2)(3x + 2)(x - 4).

plz help me or dont lol

Answers

Answer:

x = 8

Step-by-step explanation:

:)

Answer:

8

Step-by-step explanation:

I believe one of the rules of angles states that angle (4x-6) = angle (7x-30).

so 4x-6 = 7x-30

moving like terms together,

7x-4x = -6 + 30

3x = 24

x = 24/3

x = 8

What is the value of x in the equation 25x2 = 16. A. 5/4. B. 4. C. 4/5. D. 16/25

Answers

Answer:

x = ⅘

Step-by-step explanation:

For clarity, exponents should be marked with a ^.  25x² can be written as 25x^2.

25x² = 16

divide both sides by the 25

x² = 16/25

take the square root of both sides

x = √(16/25) = √16/√25 = 4/5

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