Find the Taylor polynomial
T3(x)
for the function f centered at the number a.
f(x) = xe?7x, a = 0
T3(x) = ?
============================================
Find the Taylor polynomial
T3(x)
for the function f centered at the number a.
f(x) = x + e?x, a = 0
T3(x) = ?

Answers

Answer 1

Taylor polynomial T3(x) for the respective functions, f(x) = xe\(^(-7x)\)and f(x) = x + e\(^(-x)\), centered at a = 0.

How we find Taylor polynomial?

For the first problem:

The Taylor polynomial T3(x) for the function f(x) = xe\(^\)\(^(-7x)\)centered at a = 0 is found by evaluating the function and its derivatives at x = 0 up to the third order.

By calculating the derivatives of f(x) and evaluating them at x = 0, we obtain f(0) = 0, f'(0) = 1, f''(0) = -14, and f'''(0) = 98.

Using these values, the Taylor polynomial T3(x) can be constructed as T3(x) = x - 7x\(^2\) + 49/3 x\(^3\).

This polynomial approximates the behavior of the original function f(x) around x = 0 up to the third degree.

For the second problem:

The Taylor polynomial T3(x) for the function f(x) = x + e\(^(-x)\) centered at a = 0 is obtained by evaluating the function and its derivatives at x = 0 up to the third order.

By calculating the derivatives of f(x) and evaluating them at x = 0, we get f(0) = 0, f'(0) = 1, f''(0) = 1, and f'''(0) = -1.

Using these values, the Taylor polynomial T3(x) can be written as T3(x) = x + 1/2 x\(^2\) - 1/6 x\(^3\).

This polynomial provides an approximation of the original function f(x) near x = 0 up to the third degree.

It allows us to estimate the behavior of the function and calculate its values within a certain range around x = 0.

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Related Questions

which of the following best explans why the monopolists marginal revenue is less than the sales price

Answers

Monopolists are firms that have control over the supply of a particular product or service in a market. Due to this control, they can charge higher prices than competitive firms, which can result in lower quantities sold.

One reason why a monopolist's marginal revenue is less than the sales price is due to the downward-sloping demand curve. As the monopolist increases its sales price, the quantity demanded decreases. This means that the revenue generated from each additional unit sold is lower than the revenue generated from the previous unit sold. In other words, the marginal revenue earned from each unit sold is less than the sales price. This occurs because the monopolist must lower the price of all units sold to sell additional units, which lowers the average revenue earned per unit.
To illustrate this, imagine a monopolist that sells widgets for $10 each. If the monopolist lowers the price to $9, it may sell 10 widgets, resulting in revenue of $90 ($9 x 10). However, if the monopolist maintains the $10 price and only sells 9 widgets, the revenue is $90 ($10 x 9). In this case, the marginal revenue for the 9th unit sold is $0, which is less than the sales price of $10. This is because the monopolist must lower the price of all units sold to sell the additional unit, resulting in a decrease in average revenue per unit. Overall, the monopolist's marginal revenue is less than the sales price due to the downward-sloping demand curve and the need to lower prices to sell additional units.


A monopolist, unlike firms in a competitive market, has significant market power due to the absence of competition. This allows the monopolist to control the market price of their product by adjusting the quantity supplied. When a monopolist wants to sell an additional unit, they must lower the sales price for all units, including the ones already being sold. This is because the demand curve faced by a monopolist is downward-sloping, meaning that in order to sell more units, the monopolist has to decrease the price.
Marginal revenue refers to the additional revenue gained from selling one more unit of the product. As the monopolist lowers the sales price to sell more units, two things happen: the revenue increases from the additional unit sold, but there is also a loss in revenue from the units that were sold at a higher price before the price reduction.

As a result, the marginal revenue is less than the sales price, since it takes into account not only the revenue from the additional unit sold but also the loss of revenue from lowering the price of all units. This relationship between the monopolist's pricing strategy and marginal revenue is a key factor in determining the monopolist's profit-maximizing level of output and price.

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The data in the table above was compiled by a new pet information website from a random survey of users with Basset Hounds and Welsh Corgis. Which statement best compares the height of the two breeds based on the collected data?



An adult Welsh Corgi is always going to be shorter than an adult Basset Hound.

Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.

There is no noticeable difference in the height of the two breeds since the Mean Absolute Deviation for each breed is roughly the same.

It is impossible to make a valid conclusion because the sample sizes are too small.

The data in the table above was compiled by a new pet information website from a random survey of users

Answers

Answer:

An adult Welsh Corgi is always going to be shorter than an adult Basset Hound.

Step-by-step explanation:

That's what I think because the Basset Hound is 13.8 in. in height right? So he's two inches taller if we round up both numbers. Basset hound would be 14 and welsh corgi would be 11....................okay im not sure i give up but it's either

"An adult Welsh Corgi is always going to be shorter than an adult Basset Hound."

"Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.

whichever just not the other ones good luck!

Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.

What is mean?

Mean is actually the average of all the observations.

What is absolute mean deviation?

Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.

of a data set is the average distance between each data value and the mean.

How to know which statement best compares the height of the two breeds based on the collected data?

According to the problem,

Mean height of Basset hounds is 13.8Mean height of Welsh Corgis is 11.1 Mean absolute deviation of height of Basset hounds is 1.9Mean absolute deviation of height of Welsh Corgis is 1.2

Here we can say, the average height of Basset hounds is 13.8 and is highly dispersed in comparison to Welsh Corgis

So, we can say Basset hounds tend to be a little over two inches taller than Welsh Corgis, but have a higher variability in height.

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Matilda asked 20 random people in the street if they would like to discuss what they want to do during the summer break. seven of them said yes. how is this sample biased? the people who chose to participate might not be similar to the people who didn’t. she should have asked more people. she should have asked girls only. the number of people who agreed was too small.

Answers

The sample is biased because sample size is too small. So option (1) she should have asked more people is the correct answer.

Sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. Sampling bias occurs when some members of a population are systematically more likely to be selected in a sample than others.

For the given situation,

Sample size = 20

Here Matilda have surveyed only 20 people. Since it is a less value, the sample is biased.

We could not take as the population suggestion with the suggestion of only seven people.

To know the population's liking's, Matilda should have asked more people in the street if they would like to discuss what they want to do during the summer break asked more number of people in the population.

Hence we can conclude that the sample is biased because sample size is too small. So option (1) she should have asked more people is the correct answer.

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a diver was collecting water samples from a lake. he collected a sample at every 3m, starting at 5m below water surface. the final sample was collected at a depth of 35m.how many sample did he collected​

Answers

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

Decide !!!!!!!!!!!!!!!!!!

Decide !!!!!!!!!!!!!!!!!!

Answers

Make note of the coefficients in the first and fourth equations. They've been conveniently picked so that subtracting one equation from the other eliminates every variable but t. We have

(3r + 2s + t + 2u + 3v) - (3r + 2s + 3t + 2u + 3v) = 7 - 17

-2t = -10

t = 5


Explain how to use the regression calculator to make a reasonable prediction given a data table. ​

Answers

Answer:

Given bivariate data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.

Step-by-step explanation:

Answer:

Sample Answer: Given bivariate data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.

Step-by-step explanation:

its from edge

I need help ASAP!!Explain the answer

I need help ASAP!!Explain the answer

Answers

Answer:

volume=pi times r^2 height÷3.

r is the radius, or in this case 4yd. height is 10yd. pi is 3.14

Here are the steps:

3.14r^2 height÷3

3.14×4^2 10÷3

=167.55

final answer rounded to the nearest tenth: 167.6

I apologize for getting the math wrong the first time. My formula was correct, but I needed to double check my calculations. I'm certain this is the right answer.

A square is inscribed in a circle as shown below. The radius of the circle is 7 inches, and the distance from the centers of the square and circle to the edge of the square is 5 inches. What is the area, in square inches, of the shaded region? Responses A. 14π – 100 A. 14π – 100 ​B. 14π – 25 ​ B. 14π – 25 ​C. 49π – 100 ​ C. 49π – 100 ​D. 49π – 25 ​ D. 49π – 25 ​E. (72 – 52)π

Answers

the space is A there because A is the one

If you invest $3,750 at the end of each of the next six years at
1.9% p.a., how much will you have after 6 years?
Group of answer choices
$14,985
$25,471
$23,596
$33,673

Answers

If you invest $3,750 at the end of each of the next six years at an interest rate of 1.9% per annum, you will have approximately $23,596 after 6 years.

To calculate the total amount accumulated after 6 years, we can use the formula for the future value of an ordinary annuity. The formula is given as:

Future Value = Payment * [(1 + Interest Rate)^n - 1] / Interest Rate

Here, the payment is $3,750, the interest rate is 1.9% per annum (or 0.019 as a decimal), and the number of periods (years) is 6.

Substituting the values into the formula:

Future Value = $3,750 * [(1 + 0.019)^6 - 1] / 0.019

= $3,750 * (1.019^6 - 1) / 0.019

≈ $23,596

Therefore, after 6 years of investing $3,750 at the end of each year with a 1.9% interest rate per annum, you would have approximately $23,596. Hence, the correct answer is $23,596.

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find the missing side.round to the nearest tenth.

find the missing side.round to the nearest tenth.

Answers

The length of the missing side is 9.6

How to determine the length

To determine the length of the missing side, we need to take note of the following;

The six different trigonometric identities are listed thus;

tangentcotangentsecantcosecantsinecosine

From the information given, we have that;

The measure of the angle is 53 degrees

The length of the opposite side of the angle is x

The hypotenuse side of the angle is 12

Using the sine identity.

sin 53 = x/12

cross multiply the values

x = 12(0.7986)

x = 9. 6

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An item has a listed price of $45. If the sales tax rate is 5%, how much is the sales tax (in dollars)?

Answers

Answer:

$42.75

Step-by-step explanation:

what is the solution set of this inequality x < -10 i need help

Answers

Answer:

x= 1 (any number greater than -10)

Step-by-step explanation:

">" this sign shows that any number greater than -10 can be x. There is no specific answer.

Answer:

The solution set of an inequality is < (less than) or > (greater than) to compare two or more numbers. Example 12 > - 10.

Step-by-step explanation:

When comparing two numbers, like 5 and 8, you probably recognize that the number 5 is less than the number 8. You probably also realize that the number 8 is greater than the number 5. In math, we use the inequality symbols < and > to compare two or more numbers.

How do you find the x and y intercepts for linear inequalities

Answers

Answer:

the point at which your line cut your y axis is the intercept

Answer:

Alternatively, we can determine the x-intercept and the y-intercept of the standard form linear inequality by substituting y = 0, then solve for x and substituting x = 0, then solve for y respectively. Recall that the x-intercept is the value of x when y = 0 and the y-intercept is the value of y when x = 0.

hope that helps

have a great day/night

19NBoli

For box plot data where Q1 = 200, Q2 = 250, and Q3 = 290, the
IQR

Answers

The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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consider the vectors x and a and the symmetric matrix a. i. what is the first derivative of at x with respect to x? ii. what is the first derivative of xt ax with respect to x? what is the second derivative?

Answers

The first derivative of at x with respect to x is simply the transpose of the matrix a.The first derivative of xt ax with respect to x is 2ax, since taking the derivative of the product of two vectors involves multiplying one of the vectors by the derivative of the other vector, and in this case the derivative of x is the identity matrix (since x is a vector and not a matrix).The second derivative of xt ax with respect to x is simply the matrix 2a, since the second derivative involves taking the derivative of the first derivative.1. Given the vector x and the symmetric matrix A.
2. We need to find the first and second derivatives of the following expressions:
  i. A * x
  ii. x^T * A * x

The question involves vectors, symmetric matrices, and derivatives. Let's break it down step-by-step.

i. First derivative of A * x with respect to x:
To find the derivative of A * x with respect to x, we treat A as a constant matrix. The first derivative is simply the matrix A itself.

Answer: The first derivative of A * x with respect to x is A.

ii. First derivative of x^T * A * x with respect to x:
To find the first derivative of this expression, we'll use the following formula for the derivative of a quadratic form:

d/dx (x^T * A * x) = (A + A^T) * x

Since A is a symmetric matrix, A = A^T. Therefore, the formula becomes:

d/dx (x^T * A * x) = 2 * A * x

Answer: The first derivative of x^T * A * x with respect to x is 2 * A * x.

iii. Second derivative of x^T * A * x with respect to x:
The second derivative of x^T * A * x with respect to x is the derivative of the first derivative (2 * A * x) with respect to x. Since A is a constant matrix, the second derivative is zero.

Answer: The second derivative of x^T * A * x with respect to x is 0.

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A carpenter has a rectangular sign on her truck that measures
57.6 cm × 32 cm. Her 9 cm × 5 cm business cards are a smaller copy of the sign. What scale factor was used to create the business cards?

Answers

The scale factor would be a -1/3 going smaller

What is an equation of the line that passes through the points (-4, -1)and (3, -8)
Put your answer in fully reduced form.

Answers

I'm pretty sure the answer is 0 because (-4,1) - (3,-8) gets you 0

5 A line passes through the point (4, 1) and has a slope of - Write an equation in slope-intercept form for this line.​

Answers

Answer:

_______Y=0.75X-2_______

win) = 2n + 1; Find w(6)

Answers

Answer:

13

Step-by-step explanation:

w(n) = 2n + 1;

Let n = 6

w(6)= 2*6 +1

      = 12 +1

      = 13

Answer:

\(\Huge \boxed{w(6)=13}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(w(n)=2n+1\)

Replace n with 6.

\(w(6)=2(6)+1\)

Evaluating:

\(w(6)=12+1\)

\(w(6)=13\)

\(\rule[225]{225}{2}\)

suppose sin(A)=-0.78. use the trig identity sin^2(A)+cos^2(A)=1 and the trig identity tan(A) = sin(A)/cos(A) to find tan(A) in quadrant IV. round to the ten-thousandth.

a. -0.2039
b. 1.3941
c. 0.8671
d. -1.2464

Answers

In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Estimate a 15% tip on a dinner bill of $15.22 by first rounding the bill amount to the nearest ten dollars.

Answers

Answer:

2.28. Round to the nearest ten dollar is 2.3

Step-by-step explanation:

To round to the nearest tenth, u need to leave only one number after the decimal point.

Please ASAP Help
Will mark brainlest due at 12:00​

Please ASAP HelpWill mark brainlest due at 12:00

Answers

Answer: -5

Step-by-step explanation:

can someone do this one too pls

can someone do this one too pls

Answers

Answer:

31

Step-by-step explanation:

Well I'm pretty sure you just do 93 divided by 3 since three people can eat from one pizza

Answer:

32

Step-by-step explanation:  

      x96

1/3          96/3 (32)  

1               96

      x96

Multiply denominator and numerator by 96

Which one of these ordered pairs show a combination of 12 coins from the graph?



Which one of these ordered pairs show a combination of 12 coins from the graph?


(10, 2)

(5, 5)

(10, 5)

(10, 10)

Which one of these ordered pairs show a combination of 12 coins from the graph?Which one of these ordered

Answers

The ordered pair that show a combination of 12 coins from the graph is (10, 2)

How to determine the ordered pair

from the question, we have the following parameters that can be used in our computation:

The graph

The purple line represents the combination of 12 coine

Using the above as a guide, we have the following:

The equation is

x + y = 12

From the list of options, we have

(10, 2): 10 + 2 = 12

Hence, the ordered pair is (10, 2)


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HELP PLEASE I WILL GIVE 100 Poins just please and brainliest

HELP PLEASE I WILL GIVE 100 Poins just please and brainliest

Answers

Answer: ok i dont really know but ask your teacher for help

Step-by-step explanation:

Find the value of the variables

Find the value of the variables

Answers

Answer:

x = 121 degrees

y = 59 degrees

w = 59 degrees

z = 53 degrees

v = 121 degrees

Step-by-step explanation:

31 + 90 + w = 180  ==> these three angles are in the top left triangle.

                                    Triangles add up to 180 degrees

121 + w = 180  ==> solve for w

w = 59 degrees

y = w ==> these angles are opposite adjacent angles; they are congruent

y = 59 degrees ==> Both angles are equal. So both angles are 59 degrees

68 + y + z = 180 ==> triangles add up to 180 degrees

68 + 59 + z = 180 ==> plugin 59 for y

127 + z = 180 ==> solve for z

z = 53 degrees ==> subtract 137 on both sides

w + x = 180  ==> w and x are on a straight line.

                           Straight lines add up to 180 degrees.

59 + x = 180  ==> plugin 59 for w

x = 121 degrees  ==> subtract 59 on both sides

v + y = 180 ==> v and y are also on a straight line.

v + 59 = 180 ==> plugin 59 for y

v = 121 degrees ==> subtract 59 on both sides

x = 121 degrees

y = 59 degrees

w = 59 degrees

z = 53 degrees

v = 121 degrees

Write the coordinates of the vertices after a rotation 90 degrees counterclockwise around the origin.

Write the coordinates of the vertices after a rotation 90 degrees counterclockwise around the origin.

Answers

Answer: J' (8, -9); K' (8, -2); L' (3, -2); M' (3, -9)

Step-by-step explanation:

A rotation of 90 degrees counterclockwise is (x, y) -> (-y, x), so

J (-9, -8) -> J' (8, -9)

First, you take negative 8 (y) of J and make it positive 8 for the x of J'. Then, take -9 (y) of J and switch it to x of J'.

You repeat this process for the rest of the points. X switches to Y with the opposite sign and Y switches to X but stays the same.

K (-2, -8) -> K' (8, -2)

L (-2, -3) -> (3, -2)

M (-9, -3) -> (3, -9)

when you add 2+2 is it fish?

Answers

Answer:

So when you add 2 plus to it equals 2 adrew tates kissing.

Step-by-step explanation:

Please help‼️ domain and range‼️

Please help domain and range

Answers

The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

Calculating the domain and range of the graph?

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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The number a is less than the number b by 1/5 of b. By what part of a is b greater than a?

Answers

Answer:

b is greater than a by 1/4 of a

Step-by-step explanation:

The statement “The number a is less than the number b by 1/5 of b”

means “if we subtract one fifth of b from b itself we get a”

we write this mathematically like this :

\(a=b-\frac{b}{5}\)

_________

\(\rightarrow a = \frac{5b-b}{5} =\frac{4b}{5}\)

\(a=\frac{4b}{5} \Longrightarrow 5a=4b\)

\(5a=4b\Longrightarrow b=\frac{5a}{4}\)

\(\Longrightarrow b=\frac{5a}{4} =\frac{4a+a}{4}=\frac{4a}{4}+\frac{a}{4}=a+\frac{a}{4}\)

Answer:

0.25

Step-by-step explanation:

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