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



The equation of a curve is
[tex]y = 4x {}^{3} + 4px {}^{2} + 16x - 9[/tex]
Find the range of values of p such that y is an increasing function.

Answers

Let's solve for p.

[tex]y=4x3+4px2+16x−9[/tex]

Step 1: Flip the equation.

[tex]4px2+4x3+16x−9=y[/tex]

Step 2: Add -4x^3 to both sides.

[tex]4px2+4x3+16x−9+−4x3=y+−4x3[/tex]

[tex]4px2+16x−9=−4x3+y[/tex]

Step 3: Add -16x to both sides.

[tex]4px2+16x−9+−16x=−4x3+y+−16x[/tex]

[tex]4px2−9=−4x3−16x+y[/tex]

Step 4: Add 9 to both sides.

[tex]4px2−9+9=−4x3−16x+y+9[/tex]

[tex]4px2=−4x3−16x+y+9[/tex]

Step 5: Divide both sides by 4x^2.

4px² / 4x² = −4x³ − 16x + y + 9 / 4x²

Answer:

p = −4x³ − 16x + y + 9 / 4x²

if the mean of 6 7 13 and 10 is 8 find the range ​

Answers

Answer:

hope this hlo u

Step-by-step explanation:

range =highest observation-lowest observation

range=10-6

=4

Highest number - lowest number

13-8
5

In the chemical formula 2SO2, how many total atoms of oxygen (O) are there?​

Answers

Answer:

4

Step-by-step explanation:

2 molecules of SO2

each molecule contains 2 atoms of Oxygen

Answer:

Step-by-step explanation:

Can y’all help me with this

Answers

Answer:

24.45cm squared

Step-by-step explanation:

(9 x 12) - ((6 x 3.14) / 2)

43 decreased by a number B

Answers

Answer:

43 - B = x

Step-by-step explanation:

When decreasing, you are subtracting, so the equation for this problem would be 43 minus B equals whatever quantity you were given as a solution.

Subract the sum of 3a^4b-4b^3+c^2 & 6a^4b+3b^3-6c^2 from the sum of 6a^4b-4b^3-4c^2 & 2a^4b+4b^3+7c^​

Answers

Answer:

-a^4b + b^3 - 8c^2

Step-by-step explanation:

Sum of

3a^4b-4b^3+c^2 + 6a^4b+3b^3-6c^2

= 3a^4b + 6a^4b - 4b^3 + 3b^3 + c^2 - 6c^2

= 9a^4b - b^3 - 5c^2

Sum of

6a^4b-4b^3-4c^2 + 2a^4b+4b^3+7c^

= 6a^4b + 2a^4b - 4b^3 + 4b^3 - 4c^2 + 7c^2

= 8a^4b + 3c^2

Subtract

8a^4b + 3c^2 - (9a^4b - b^3 - 5c^2)

= 8a^4b + 3c^2 - 9a^4b + b^3 + 5c^2

= 8a^4b - 9a^4b + b^3 + 3c^2 + 5c^2

= -a^4b + b^3 - 8c^2

Convert the following repeating decimal to a fraction in simplest form.
.6

Answers

Answer:

2/3

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

0.6 is a repeating decimal in this case, so you can round it to .7

From there, you simply put it over ten because you cant break seven down any more than that in a simple fraction.

Find the slope of the line through each pair of points




(-20,-4), (-12,-10)​

Answers

Answer:

is it just the slope of those points? if so -3/4

Step-by-step explanation:

i think. if not correct me

Answer:

[tex]-\frac{3}{4}[/tex]

Step-by-step explanation:

The slope of a line is given by:

[tex]m=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, the slope of the line that passes through these points is:

[tex]m=\frac{-10-(-4)}{-12-(-20)}=\frac{-6}{8}=\fbox{$-\frac{3}{4}$}[/tex].

A video game is on sale for $55. If the discount was
14%, what was the original price?

Answers

Answer:

$77

Step-by-step explanation:

i just take 55 x 0.14 which is 7.7 then i moved the decimal 1 place to the right.

Answer:

I believe the answer it 62.70

although I am not completely sure

Step-by-step explanation:

14% of 55 = 7.7

7.7 + 55 = 62.7

= $62.70

share $180 between anna and barry so that Anna share to barry share is in the ratio 4:5​

Answers

Answer:

Anna: $80

Barry: $100

Step-by-step explanation:

total of 9 shares

each 20 dollars

4(20) = 80

5(20) = 100

Consider two people where one person is 25% taller than the other but proportion in exactly the same way That the taller person looks like a lager version of the shorter person Suppose the shorter person has a 36%-inch waist what size is the the taller person's waist?

Answers

Answer:

46.8 inches

Step-by-step explanation:

Taller person = 30% more than height of shorter individual

Waist size of shorter person = 36 inches

Since they are proportioned in the same way:

Waist size of the taller person will be 30% larger than the waist size of the shorter person :

30% increase in size 36

(100 + 30)% of 36

130% of 36

(130 / 100) * 36

1.3 * 36

= 46.8 inches

Please help!!
How do I rewrite this expression into radical form??

Answers

i think this should be right

Mini made a recipe that yields 4 and 1 over 2 cups. If each serving is 1 over 2 cup, which expression will help Mini determine the number of servings her recipe will yield?

Answers

Answer:

1/2x = 4 1/2

Where x = Number of servings = 9 servings

Step-by-step explanation:

Mini made a recipe that yields 4 and 1 over 2 cups.

1 recipe = 4 1/2 cups

1 serving = 1/2 cups

1/2 cups = 1 servings

4 1/2 cups = x servings

Cross Multiply

1/2 × x = 4 1/2

x = 4 1/2 ÷ 1/2

x = 9/2 ÷ 1/2

x = 9/2 × 2

x = 9 servings.

Therefore, the expression tha will help Mini to determine the number of servings her recipe will yield is

1/2x = 4 1/2

Where x = Number of servings = 9 servings

Can someone please explain to me how I would do this, I cannot figure out how to do this equation at all!!

Answers

Answer:

First, do 4x*4x. then,16x*16x. next, 64x*64x. and,256x*256x. answer:1024x. Divide 1024x by 8x. answer to that is 128.

Answer:

The expression in simplified form:

[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]

Step-by-step explanation:

Given the expression

[tex]\frac{4x^5}{8x}[/tex]

We need to simplify the expression.

Simplifying the expression

[tex]\frac{4x^5}{8x}[/tex]

Cancel the common factor: 4

[tex]=\frac{x^5}{2x}[/tex]

Cancel the common factor

[tex]=\frac{x^4}{2}[/tex]

Therefore, the expression in simplified form:

[tex]\frac{4x^5}{8x}=\frac{x^4}{2}[/tex]

Albert, bill, claire, and David are all siblings. Bill was born 2 years after Albert. Claire's favourite colour is orange and she is currently half the age of Albert. David enjoys golf and swimming and he is 3 times older than Bill.

The total of their age is 113 using algebraic methods find out their exact age
what is their exact age

Answers

Answer:

Albert = 22

Bill = 22 - 2 = 20

Claire = 22/2 = 11

David = 3(20) = 60

Step-by-step explanation:

Let Albert's age = x

Bill = x - 2

Claire = x/2

David = 3(x - 2)

Total sum of their ages = 113

x + x - 2 + 0.5x + 3(x - 2) = 113

x + x - 2 + 0.5x + 3x - 6 = 113

x + x + 3x + 0.5x -2 - 6 = 113

5.5x - 8 = 113

5.5x = 113 + 8

5.5x = 121

x = 121 / 5.5

x = 22

Albert = 22

Bill = 22 - 2 = 20

Claire = 22/2 = 11

David = 3(20) = 60

make x the subject. 4x-5=t(x+m)

Answers

Answer:

x= tm+5/4-t

Step-by-step explanation:

4x-5=t(x+5)

4x-5-=tx+tm   distributive

4x-5-tx=tm    substract tx from both sides

4x-tx=tm+5   add 5 to both sides

x * 4+ x(-t) =tm+5  factor x out 4x-tx

x(4-t)=tm+5   factor x out x*4 + x(-t)

x(4-t)/4-t= tm/4-t+ 5/4-t   divide each term in 4-t

x= tm/4-t + 5/4-t combine the numerators over the common denominator

x=tm+5/4-t

3 (m+6) +7 (m-2)


7(6x + 5) - 8


4(3x + 5) - 13


Answers

Answer:SAME SIGNS 1. Add.

2. Sum is positive if both are positive; negative if both are negative.

  5 + 8 = 13 –5 + (–8) = –13

 DIFFERENT SIGNS

1. Subtract the absolute values.

2. Answer is sign of the integer with the greater absolute value.

   5 + (–8) = –3 –5 + 8 = 3

Find each sum. 1. –4 + (–8)

–12

4. –16 + 11 –5

7. –49 + (–32)

–49 –81 –32 –81

2. 14 + 16 30

5. 28 +(–42) –14

8. 23 + (–23) 0

3. –43 + (–12) –55

6. 75 + (–5) 70

9. 86 + (–18)

86 68–18 68

       

Integers

Multiplying & Dividing

  RULE

EXAMPLES

 1. Multiply or divide.

2. The answer is positive if the signs are the same (both positive or both negative); negative if the signs are different (one positive and one negative).

  –5 x(–8) = 40 40  4 = 10

 16 x(–3) = –48 –20  10 = –2

Find each product or quotient.

1. –3 x (–8) 24

4. 0 x (–121)

0 5 –13

2. –5 x (–5) 25

3. –15 x 3 –45

  5. –35 (–7)

6. –65  5

  7. 240  (–4) 8. 36  12 9. (–49  7) x 8 –7 x 8

 –60 3

–56

Step-by-step explanation:

Please help me with this question!!

Answers

Step-by-step explanation:

according to pythagoras theorem

Hypotenuse2 = Perpendicular2 + Base2

c2 = a2 + b2

therefore,

x2 = (4)2 + (4)2

x2 = 16 + 16

x2 = 32

x = √32

hence, x = 4√2


Consider the volume of a rectangular pyramid, one whose base is not square. Does changing one of the three variables (length, width, or helght)
by a given fraction have a greater effect on the volume of the pyramid than changing either of the other two variables? That is, which variable, if
any, has the largest influence on the volume? Assume that the other two variables remain constant. Explain your answer.

Answers

Answer:

dobt worry il heñp il solve

Pleaseee help this is urgent!!! I need it in English! Please show all the work ! 14 points

Answers

Answer:

width = 40 feet, length = 90 feet

Step-by-step explanation:

length = 2w + 10

width = w

Perimeter = 260

Perimeter of rectangle = 2length + 2width

Sub the values into that equation:

260 = 2(2w + 10) + 2(w)

260 = 4w + 20 + 2w

260 = 6w + 20

260 - 20 = 6w

240 = 6w

w = 240/6

w = 40

So now we know the width of the garden is 40 feet.

To find the length, substitute the width into the length equation:

length = 2w + 10

length = 2(40) + 10

length = 90 feet

length = 90 feet, width = 40 feet

I REALLY NEED HELP ON THIS!!!!!! I WILL MARK BRAINLIEST

Answers

Answer:

y = 2,500x + 5,000

Rate of change = $2500 a year

Initial value = $5000

Step-by-step explanation:

We have 3 values to figure what is the function here, the rate of change, and the initial value.

To find the initial value, find where y is located where x is 0. In this case it's $5000, so that's the initial value.

Now the rate of change. Find y where x is 1. That is $7,500. Subtract $5000 from to get the rate of change, since it's the same. It's constant because of a straight diagonal line.

$7,500 - $5,000 = +$2,500/year

Now the equation. This is not proportional, because y's starting point is not 0. It's greater than that, so an addition sign is in the equation. Do you remember our initial value? That's right! It was $5,000, so put that after the addition sign.

y = ????x + 5,000

You also need to remember the rate of change, which was 2,500. Put that on the left of the addition sign and there's your equation!

y = 2,500x + 5,000

Answer:

y=2500x + 5000

2500

5000

Step-by-step explanation:

What is the slope of the line with equation y - 3= -1/2(x - 2)

Answers

If u use the equation y=mx+b with m being the slop and b being the y-intercept.

Answer:

-1/2

Step-by-step explanation:

according to what I learnt, the general form of every equation is y=mx+c where y is the y value, x is the x value, m is the slope and c is the y-intercept so the equation y-3= -1/2(x - 2) in the general form wil be :

y= -x/2+4 and so m= -x/2 ,that is -1/2

You have 42 coins with a total value of $3.00. Some of the coins are dimes, and the rest are quarters.

Select the two equations that would create the best system of equations to represent this scenario.

Answers

Answer:

1. $3.00+42=$3.42

2. 4 Dimes , 2 Pennies

Step-by-step explanation:

2. 4 Dimes = 40 cents , 2 pennies = 2 cents

1. Add up 3.00+42 and that is how you could get the answer for number 1 .

△RST ~ △RYX by the SSS similarity theorem.

Which ratio is also equal to StartFraction R T Over R X EndFraction and StartFraction R S Over R Y EndFraction?

StartFraction X Y Over T S EndFraction
StartFraction S Y Over R Y EndFraction
StartFraction R X Over X T EndFraction
StartFraction S T Over Y X EndFraction

Answers

Answer:

Answer would most likely be option D. StartFraction S T Over Y X EndFraction

Explanation:

Take care..

Find the Values of y
Y ² = 169

Answers

Answer:

Y= 13,-13

Step-by-step explanation:

A is what percent of B? Pls help???

Answers

Answer:

If you want to know what percent A is of B, you simple divide A by B, then take that number and move the decimal place two spaces to the right. That's your percentage!

Step-by-step explanation: There is no exact answer and it would be null. You didn't even give an image

i dont know plz help

Answers

7/10 more blueberry muffins then the pumpkin muffins .

HELP I NEED HELP ASAP

Taxi Driver A(x)=1.50x+5 and Taxi Driver B charges B(x)=1.25x+8 where x is the number of miles driven. After how many miles will the cost be the same for each taxi driver?

Answers

Answer:

12 miles

Step-by-step explanation:

1.25x + 8 =1.5x+5

1.25x-1.5x=5-8

-0.25x=-3

-0.25x/-0.25x=-3/-0.25

x= 12

Help me out with this, homes

Answers

Answer:

2

Step-by-step explanation:

2

PLEASE HELP MEEEE!!!!!!!

Answers

Answer:

its a black picture...?

Step-by-step explanation:

help with what- theres no problem its black
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