find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x → (⁄2) cos(x) 1 − sin(x)

Answer:

-4

Step-by-step explanation:

plug in 3 for x

2(3)-10

6-10

=-4

Answer:

\( - 3c - 8\)

Step-by-step explanation:

1) Collect like terms.

\((6c - 9c) - 8\)

2) Simplify.

\( - 3c - 8\)

Therefor, the answer is -3c - 8.

Selling price = $6.37 .

Selling price = $6.94

Selling price = $346.80

1)

Sales revenue = 6,000

Less:-Variable costs ($1.5 per unit 1,000) = 1,500

Less:- Fixed costs = (1,700)

Operating Income = 2,800

Variable costs and Fixed costs have increased.

Hence, in order to maintain the same Operating Income, the selling price should be higher than the current selling price .

Thus to maintain same operating income the selling price should be $6.37 .

2)

The computation is given below:

Sales price = ( Total sales revenue ÷ packages sold)

Total sales revenue = ( Total Cost + Operating income )

Total Cost = ( Variable Cost + Fixed cost)

Now

Variable cost = 1,000 packages × $1.90 per unit

= $1,900

Fixed cost = $1,700 × 120%

= $2040

Total cost = $1,900 + $2,040

= $3,940

Now  

Total sales revenue is

= $3,940 + $3,000

= $6,940

Now  

Sales price = $6,540 ÷ 1,000 packages

= $6.94

3)

-Fruit Computer Company has variable costs of $220 per unit and fixed costs of $32,000 per month.

- The company currently sells 500 units per month at a sales price of $300.

Net margin = $8000

- The company wants to increase its operating income by 30%.

- If the company upgrades the computer quality, the variable cost per unit will increase to $240 and the fixed costs will rise by 50%.

Thus the selling price per unit will be  $346.80 per unit.

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The sine function with the values in the table is defined as follows:

y = 5sin(πx/2) - 1.

The standard definition of the sine function is given as follows:

y = Asin(B(x - C)) + D.

For which the parameters are given as follows:

The function has a maximum value of 4 and a minimum value of -6, for a difference of 10 units, hence the amplitude is obtained as follows:

A = [4 - (-6)]/2

A = 10/2

A = 5.

Without vertical shift, a function with amplitude of 2 would oscillate between -5 and 5, while this one oscillates between -6 and 4, hence the vertical shift is given as follows:

D = -1.

The shortest distance between repetitions can be given by 4 - 0, hence the period is of 4 units and the coefficient B is given as follows:

2π/B = 4

B = 2π/4.

B = π/2.

The function is at it's midline at the origin, hence it has no phase shift, and thus the equation is given as follows:

y = 5sin(πx/2) - 1.

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Answer:

yes they are

Step-by-step explanation:

triangle ️ WXY has angles 90 and 56. to find the last angle 180-(90+56) = 34 degrees.

triangle ️ JKL has angles 90 and 34. To find last angle 180-(90+34) = 56 degrees.

since all 3 angles on the 2 triangles are equal the triangles are congruent.

Using the subtraction operation, the baby gained a total weight of 3.25 pounds.

Subtraction operation is one of the four basic mathematical operations, including addition, division, and multiplication.

Subtraction involves the minuend, the subtrahend, and the difference.

The total weight of the baby during its first year of life = 11 pounds

The weight gained during the first four months = 4.25 pounds

The weight gained during the second four months = 3.5 pounds

The weight of the baby gained during the last four months = 3.25 pounds (11 - 4.25 - 3.5).

Thus, by subtraction, we can conclude that the baby gained 3.25 pounds in weight during the last four months of its life.

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The standard deviation for the given Poisson distribution is 0.8.

A Poisson distribution is used to model the number of events occurring in a fixed time interval when the events occur independently and at a constant rate. The mean and variance of a Poisson distribution are equal, and both are given by λ, the rate parameter.

Here, the given information is that the company receives an average of 0.64 purchase orders per minute. Therefore, λ = 0.64.

The formula for the variance of a Poisson distribution is σ² = λ, where σ is the standard deviation. Thus, substituting λ = 0.64 in this formula, we get σ² = 0.64. Taking the square root of both sides, we get σ = √0.64 = 0.8.

Therefore, the correct answer is 0.8.

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Answer:

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

Answer:

????

Step-by-step explanation:

The graph of this equation is a straight line with slope 1 and y-intercept 2sqrt(2), passing through the second and fourth quadrants of the Cartesian plane.

To replace the polar equation r cos theta + r sin theta = 4 with an equivalent Cartesian equation, we can use the trigonometric identity cos theta + sin theta = sqrt(2)sin(theta + pi/4). So, we have r(sqrt(2)sin(theta + pi/4)) = 4.
Now, we can substitute r with sqrt(x^2 + y^2) and sin(theta + pi/4) with (y+x)/sqrt(x^2 + y^2) to get the Cartesian equation:
sqrt(x^2 + y^2) * (y+x)/sqrt(x^2 + y^2) = 4/sqrt(2)
which simplifies to
x + y = 2sqrt(2)
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Answer:

68 are not blue

Step-by-step explanation:

it's in the pic above if u need the steps.

The two number of rivers that run through the Fertile Crescent are the Tigris and the Euphrates.

These rivers were positive for societies in the Fertile Crescent because they provided a reliable number of  source of water for irrigation and drinking, and their associated river basins provided a variety of resources including fish, plants, and minerals. However, the rivers were also negative for societies in the Fertile Crescent because they could be unpredictable and cause flooding and erosion, which could destroy homes and crops.

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Answer:

The two rivers that run through the Fertile Crescent are the Euphrates and the Tigris. The rivers are the reason that the region is referred to as “fertile”. A fertile region is an area that produces healthy, sustaining vegetation. The negative aspect of the rivers was that flooding was common. Flooding could wipe out an entire years crop.

Step-by-step explanation:

pictures below

A trigger strategy is a strategy that specifies an action to take in response to certain observed actions by other players. In this context, a trigger strategy involves cooperating as long as the other player cooperates, but immediately defecting and pursuing a different strategy if the other player deviates from cooperation.

In the given game, the firms cannot attain the joint profit-maximizing outcome in a subgame perfect equilibrium using trigger strategies because there is no trigger that can effectively sustain cooperation in the repeated game. Both firms have an incentive to deviate and lower their price to increase their own profit.

A stick and carrot strategy combines punishment for deviating from cooperation (stick) and rewards for cooperating (carrot). In this case, a stick and carrot strategy could involve punishing the deviating firm by setting a low quantity or price in response to their deviation, while rewarding cooperation by maintaining high quantities and prices. However, it is unlikely to attain the joint-profit maximizing outcome in a subgame perfect equilibrium using stick and carrot strategies because the firms still have an incentive to deviate and lower their price to increase their own profit, even if they face punishments or rewards. Therefore, sustaining cooperation and achieving the joint-profit maximizing outcome is challenging in this repeated game.

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The scale factor for the given dilation transformation is 1/3

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, a triangle ABC is being dilated to form a new triangle A'B'C'

We are asked to the scale factor,

The length of sides of triangle ABC is 6 units

And, length of sides of triangle A'B'C' is 2 units,

Since, the figure id shrinking, therefore, the dilation is a reduction, and scale factor must be less than 1,

Scale factor = 2/6

= 1/3

Hence, the scale factor for the given dilation transformation is 1/3

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The number one more than 79 is 80.

Number:

Numbers are mathematical objects used for counting, measuring, and labeling. The original example is the natural numbers 1, 2, 3, 4, etc. [1] Numbers can be linguistically represented by numerals. More generally, individual numbers can be represented by symbols called digits. For example, "5" is the number representing the number five. Since only a relatively small number of symbols can be remembered, basic numbers are usually organized into number systems, which are systematic ways of representing each number. The most common number system is the Hindu-Arabic number system, which can represent any number using combinations of 10 basic numeral symbols called digits.  In common parlance, a number is indistinguishable from the number it represents.

Greater than Number:

It is a mathematical term used to compare two quantities and to establish a relationship between two quantities in which one term is greater than the other. The terms greater than, less than, and equal are used to compare two numbers, amounts, or amounts. Each term has a separate letter. B. "greater than" is represented by ">", "equal to" is represented by "=", and "less than" is represented by "<".

According to the Question:

To better understand this question,

It can be expressed as 1 more than 79, 1 more than 79, 1 more than 79, 79 plus 1.

Thus,

1 more than 79 is the same as 79 plus 1. So the answer for 1 greater than 79 is calculated as:

Therefore,

1 + 79 = 80.

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Answer:

The formula for finding the area of a trapezoid is ×h

Start by substituting the values given in the problem into the formula

×4

Now Simply/solve

×4

6×4

24

The area of the trapezoid is 24

I hope this helps!!!

Step-by-step explanation:

Let x be the temperature of a freezer; at a restaurant, all the freezers are set to a temperature that is below 3°F. The inequality x < 3 is used to denote temperatures below 3°F. Hence, Option C is correct.

The occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality. To different people and in various settings, the word "inequality" may indicate different things.

In mathematics, various signs are used to denote the inequality among values.

Therefore, inequality x < 3 is used to denote temperatures below 3°F. Option C is correct.

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The completely simplified expression is( 7n 14)/( 6η).    

To simplify the expression( n 2)/( 6η/ 7),

we can start by dividing the numerator by the denominator. This is original to multiplying the numerator by the complementary of the denominator  n 2) *( 7/ 6η)

Next, we can distribute the( 7/ 6η) to both terms in the numerator ( n)/( 6η) 7( 2)/( 6η)

This simplifies to  7n/( 6η) 14/( 6η)

Now, since the two terms in the numerator have a common denominator, we can combine them ( 7n 14)/( 6η).

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Answer:

BC = 22

Step-by-step explanation:

This is an isosceles triangle.

2x - 24 = x - 2

2x = x - 2 + 24

2x = x + 22

2x -x = 22

x = 22

Answer:

x = 22

Step-by-step explanation:

Since ∠ B = ∠ C then the triangle is isosceles with 2 legs congruent , that is

AC = AB , substitute values

2x - 24 = x - 2 ( subtract x from both sides )

x - 24 = - 2 ( add 24 to both sides )

x = 22

Answer:

75:25:100

Step-by-step explanation:

The values in the table have constant second differences.

So, the relationship is a quadratic relationship.

A polynomial function with one or more variables, where the largest exponent of the variable is two, is referred to as a quadratic function. In other terms, a "polynomial function of degree 2" is a quadratic function.

Given:

The following table shows a relationship.

x    f(x)

4      325

6      388

8      437

10     472

23.1    493

12       500

The first difference;

388 - 325 = 63

437 - 388 = 49

472 - 437 = 35

493 - 472 = 21

500 - 493 = 7

The second difference;

49 - 63 = -14

35 - 47 = -14

21 - 35 = -14

7 - 21 = -14

The second difference is constant.

Therefore, the relationship is quadratic.

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3y + 20 = 3 + 2y

1y + 20 = 3

y = -17

Answer:

\(y=-17\)

Step-by-step explanation:

\(3y+20=3+2y\)

Start by subtracting 20 from each side...

\(3y+20-20=3+2y-20\\3y=2y-17\)

Now, subtract "2y" from each side...

\(3y-2y=2y-2y-17\\y=-17\)

Next, let's substitute -17 for y in the original equation to check our answer...

\(3(-17)+20=3+2(-17)\\-51+20=3+(-34)\\-31=3-34\\-31=-31\rightarrow Correct!\)

Therefore the answer is:

\(y=-17\)

In this case, we curl our fingers from u towards v and then rotate them towards v. Therefore, the direction of u × v is into the screen.

To find |u × v|, use the formula u * v = |u × v|. If u × v is directed into the screen, then |u × v| will be positive, and if u × v is directed out of the screen, then |u × v| will be negative.

The question requires us to find the value of |u × v| and also to determine whether u × v is directed into or out of the screen. Let u = <3, -4, 2> and v = <1, 5, -6>.

The cross product of two vectors u and v is given by the determinant: | i j k | | 3 -4 2 | | 1 5 -6 | = i (20 - (-12)) - j (6 - 2) + k (-15 - (-12))= 32 i - 4 j - 3 k, therefore, u × v = <32, -4, -3>. As we know, |u × v| = √(32^2 + (-4)^2 + (-3)^2)= √1089 = 33. We can use the right-hand rule to determine whether u × v is directed into or out of the screen.

According to the right-hand rule, the direction of the cross product u × v is given by curling the fingers of the right hand in the direction of u and then rotating them towards v. The thumb then points in the direction of u × v.

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a. The equation that relates M and J to the total yield can be written as 16,000 M + 14,500 J = 120,000

b. the equation relating M and J is 116.36 M + 454.55 J = 1,070,000.

An equation is a mathematical statement that asserts that two expressions have the same value, usually separated by an equal sign. It typically includes variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.

a. The total yield of the plantation is the sum of the yield of the Macintosh and Jonathan apple trees. Since the yield of Macintosh apple trees is 16,000 pounds per acre and the yield of Jonathan apple trees is 14,500 pounds per acre, the equation that relates M and J to the total yield can be written as:

16,000 M + 14,500 J = 120,000

b. The total value of the apples produced is the sum of the value of the Macintosh apples and the value of the Jonathan apples. Since Macintosh apples sell for $650 per metric ton and Jonathan apples sell for $700 per metric ton, the equation relating M and J can be written as:

(16,000 M / 2200) x 650 + (14,500 J / 2200) x 700 = 1,070,000

Simplifying the equation, we get:

116.36 M + 454.55 J = 1,070,000

Therefore, the equation relating M and J is 116.36 M + 454.55 J = 1,070,000.

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The values we get are

sin m ≈ 0.1831

cos m ≈ 0.2333

tan m ≈ 4.3496

To determine the ratios of sine (sin m), cosine (cos m), and tangent (tan m) for angle m, we need to use the given side lengths of the triangle.

Given:

Side lengths of the triangle: √851, 7, and 30

To find the ratios, we can use the definitions of the trigonometric functions:

sin m = opposite/hypotenuse

cos m = adjacent/hypotenuse

tan m = opposite/adjacent

Using the side lengths of the triangle, we can determine the ratios:

sin m = √851/30

cos m = 7/30

tan m = √851/7

Now, let's calculate the exact values and their four-decimal approximations:

sin m ≈ √851/30 ≈ 0.1831

cos m ≈ 7/30 ≈ 0.2333

tan m ≈ √851/7 ≈ 4.3496

Therefore, the ratios for sin m, cos m, and tan m are approximately:

sin m ≈ 0.1831

cos m ≈ 0.2333

tan m ≈ 4.3496

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Answer:

Simplified it would be 11x^2y^2 - 4xy^

Answer:

11x²y³ - 4xy²

Step-by-step explanation:

is the answer if simplified.

For this data, the IQR is a superior measure of variability because it is less than the range. The greatest way to quantify variability is the IQR, and that number is 11.

The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.

The median (middle value) of the lower half and upper half of the data should be found first in order to determine the interquartile range (IQR). The quartile 1 (Q1) and quartile 3 values are these (Q3). The IQR is the difference between Q3 and Q1.

From the given stem-and-leaf plot, we can see that the lowest score is 5, and the highest score is 23. Therefore, the range of the data is:

Range = highest value - lowest value = 23 - 5 = 18

We also need to find the quartiles to calculate the IQR. The median (Q2) of the data is 18, which is the value that separates the lower 50% of the scores from the upper 50%. To find Q1 and Q3, we can split the lower and upper halves of the data, respectively, and find their medians.

The lower half of the data is: 5, 10, 13, 17, 18. The median of this half is (13 + 17)/2 = 15.

The upper half of the data is: 24, 26, 28. The median of this half is 26.

Therefore, Q1 = 15 and Q3 = 26, and the IQR is:

IQR = Q3 - Q1 = 26 - 15 = 11.

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Answer:

IQR 18.5

Step-by-step explanation:

I took the test

The coefficient a₁ is 0, and the sine coefficient b₁ is also 0. The function f(x) is an even function (symmetric about the y-axis), the sine coefficient (b₁) will be zero.

The given function f(x) is defined as follows:

f(x) =

-2       for -3 ≤ x < -2

2x^2    for -2 ≤ x < 2

To determine the Fourier series coefficients ao, a₁, and b₁, we need to find the average value (ao), the cosine coefficients (a₁), and the sine coefficients (b₁) for the given function over one period.

The average value (ao) can be calculated as:

ao = (1/T) ∫[x₁ to x₁+T] f(x) dx

In this case, the period is T = 4, so we need to evaluate the integral over one period:

ao = (1/4) ∫[-2 to 2] f(x) dx

Splitting the integral into the two regions:

ao = (1/4) [(∫[-2 to -3] -2 dx) + (∫[-2 to 2] 2x^2 dx)]

Simplifying the integrals:

ao = (1/4) [(-2 * (-3 - (-2))) + (2 * ∫[-2 to 2] x^2 dx)]

ao = (1/4) [2 + 2 * (∫[-2 to 2] x^2 dx)]

The integral ∫[-2 to 2] x^2 dx can be evaluated as follows:

∫[-2 to 2] x^2 dx = [(1/3) * x^3] [-2 to 2]

∫[-2 to 2] x^2 dx = (1/3) * [(2^3) - ((-2)^3)]

∫[-2 to 2] x^2 dx = (1/3) * (8 - (-8))

∫[-2 to 2] x^2 dx = (1/3) * 16

∫[-2 to 2] x^2 dx = 16/3

Substituting this value back into the expression for ao:

ao = (1/4) [2 + 2 * (16/3)]

ao = (1/4) [2 + (32/3)]

ao = (1/4) [(6/3) + (32/3)]

ao = (1/4) * (38/3)

ao = 38/12

ao = 19/6

The coefficient ao is 19/6.

Next, we need to find the cosine coefficient (a₁) and the sine coefficient (b₁). Since the function f(x) is an even function (symmetric about the y-axis), the sine coefficient (b₁) will be zero.

To calculate the cosine coefficient (a₁), we use the following formula:

a₁ = (2/T) ∫[x₁ to x₁+T] f(x) cos((2πnx)/T) dx

In this case, n = 1 (first harmonic) and T = 4 (period). Evaluating the integral:

a₁ = (2/4) ∫[-2 to 2] f(x) cos((2πx)/4) dx

Splitting the integral into the two regions:

a₁ = (1/2) [(∫[-2 to -3] -2 cos((2πx)/4) dx) + (∫[-2 to 2] 2x^2 cos((2πx)/4) dx)]

Simplifying the integrals:

a₁ = (1/2) [(-2 * ∫[-2 to -3] cos((2πx)/

4) dx) + (2 * ∫[-2 to 2] x^2 cos((2πx)/4) dx)]

Integrating each term separately:

∫[-2 to -3] cos((2πx)/4) dx = [(4/π) sin((2πx)/4)] [-2 to -3]

∫[-2 to -3] cos((2πx)/4) dx = (4/π) [sin(-π/2) - sin(-3π/2)]

∫[-2 to -3] cos((2πx)/4) dx = (4/π) [-1 - (-1)]

∫[-2 to -3] cos((2πx)/4) dx = (4/π) * 0

∫[-2 to -3] cos((2πx)/4) dx = 0

∫[-2 to 2] x^2 cos((2πx)/4) dx can be solved using integration by parts:

u = x^2   =>   du = 2x dx

dv = cos((2πx)/4) dx   =>   v = (4/2π) sin((2πx)/4)

∫[-2 to 2] x^2 cos((2πx)/4) dx = [x^2 * (4/2π) sin((2πx)/4)] [-2 to 2] - ∫[-2 to 2] (4/2π) sin((2πx)/4) * 2x dx

∫[-2 to 2] x^2 cos((2πx)/4) dx = [x^2 * (4/2π) sin((2πx)/4)] [-2 to 2] - (4/2π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

Evaluating the definite integral and simplifying:

∫[-2 to 2] x^2 cos((2πx)/4) dx = [(4/2π) sin((2πx)/4) * x^2] [-2 to 2] - (4/2π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

∫[-2 to 2] x^2 cos((2πx)/4) dx = [(4/2π) sin((2π*2)/4) * 2^2] - [(4/2π) sin((2π*(-2))/4) * (-2)^2] - (4/2π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

∫[-2 to 2] x^2 cos((2πx)/4) dx = (4/π) sin(π) - (4/π) sin(-π) - (4/2π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

∫[-2 to 2] x^2 cos((2πx)/4) dx = 0 - 0 - (2/π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

∫[-2 to 2] x^2 cos((2πx)/4) dx = - (2/π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

Next, we need to evaluate

the integral ∫[-2 to 2] sin((2πx)/4) * 2x dx. Using integration by parts again:

u = 2x   =>   du = 2 dx

dv = sin((2πx)/4) dx   =>   v = -(4/2π) cos((2πx)/4)

∫[-2 to 2] sin((2πx)/4) * 2x dx = [2x * -(4/2π) cos((2πx)/4)] [-2 to 2] - ∫[-2 to 2] -(4/2π) cos((2πx)/4) * 2 dx

∫[-2 to 2] sin((2πx)/4) * 2x dx = [2x * -(4/2π) cos((2πx)/4)] [-2 to 2] + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

Evaluating the definite integral and simplifying:

∫[-2 to 2] sin((2πx)/4) * 2x dx = [2x * -(4/2π) cos((2πx)/4)] [-2 to 2] + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

∫[-2 to 2] sin((2πx)/4) * 2x dx = [2*2 * -(4/2π) cos((2π*2)/4)] - [2*(-2) * -(4/2π) cos((2π*(-2))/4)] + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

∫[-2 to 2] sin((2πx)/4) * 2x dx = (4/π) [- cos(π) + cos(-π)] + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

∫[-2 to 2] sin((2πx)/4) * 2x dx = (4/π) [-1 + 1] + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

∫[-2 to 2] sin((2πx)/4) * 2x dx = 0 + (4/π) ∫[-2 to 2] cos((2πx)/4) dx

We previously found that ∫[-2 to 2] cos((2πx)/4) dx = 0

Therefore, ∫[-2 to 2] sin((2πx)/4) * 2x dx = 0

Substituting this value back into the expression for a₁:

a₁ = - (2/π) ∫[-2 to 2] sin((2πx)/4) * 2x dx

a₁ = - (2/π) * 0

a₁ = 0

Thus, the coefficient a₁ is 0, and the sine coefficient b₁ is also 0.

To summarize:

ao = 19/6

a₁ = 0

b₁ = 0

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