use the definition of taylor series to find the taylor series (centered at c) for the function. f(x) = 7 sin x, c = 4

Answers

Answer 1

The Taylor series is a way to represent a function as a power series of its derivatives at a specific point in the domain. It is a crucial tool in calculus and its applications. The Taylor series for a function f(x) is given by:$$f(x) = \sum_{n=0}^\infty \frac{f^{(n)}(c)}{n!}(x-c)^n$$Where f^(n) (c) is the nth derivative of f evaluated at c.

In this case, we are asked to find the Taylor series centered at c=4 for the function f(x)=7sin(x).We first find the derivatives of f(x). The first four derivatives are:$f(x)=7sin(x)$;$f'(x)=7cos(x)$;$f''(x)=-7sin(x)$;$f'''(x)=-7cos(x)$;$f''''(x)=7sin(x)$;Notice that the pattern repeats after the fourth derivative. Thus, the nth derivative is:$f^{(n)}(x)=7sin(x+\frac{n\pi}{2})$Now, we can use the formula for the Taylor series and substitute in the derivatives evaluated at c=4:$f(x)=\sum_{n=0}^\infty \frac{7sin(4+\frac{n\pi}{2})}{n!}(x-4)^n$.

Thus, the Taylor series for f(x)=7sin(x) centered at c=4 is:$$7sin(x)=\sum_{n=0}^\infty \frac{7sin(4+\frac{n\pi}{2})}{n!}(x-4)^n$$.

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Related Questions

PLSSS HELPpPP URGENT

Answers

Answer:

Step-by-step explanation:

as u can see,the other acute angle is 43° and the other is also an acute angle and acute angles must not surpass until 80° meaning, the other acute angle is 47°

Given,

A right angle that means 90°.

One angle is 43°

Now,

$ \angle \: ACB = 43 \degree + \angle \:BCD $

=> 90° = 43° + BCD

=> BCD = 90° - 43°

=> BCD = 47°

Option ( A ) 47° is correct answer

Given the following information, stock? construct a value-weighted portfolio of the four stocks if you have $501,000 to invest. That is, how much of your $501,000 would you invest in each stock Stock Market Cap
OGG $52 million
HNL $76 million
KOA $19 million LIH $12 million

Answers

To construct a value-weighted portfolio, we need to allocate funds based on the market capitalization of each stock. The total market cap of the four stocks is $159 million. Therefore, OGG represents 32.7%, HNL represents 47.8%, KOA represents 11.9%, and LIH represents 7.5% of the total market cap. If we have $501,000 to invest, we should invest $163,710 in OGG, $239,430 in HNL, $59,490 in KOA, and $37,370 in LIH.

A value-weighted portfolio is a strategy that allocates funds based on the market capitalization of each stock. It means investing more in companies with a higher market capitalization and less in companies with a lower market capitalization. In this case, we calculate the percentage of each stock's market capitalization to the total market capitalization of all four stocks and allocate funds accordingly.

To construct a value-weighted portfolio of the four stocks, we should allocate funds based on the market capitalization of each stock. In this case, we allocate funds in the proportion of 32.7%, 47.8%, 11.9%, and 7.5% for OGG, HNL, KOA, and LIH, respectively. This ensures that we invest more in companies with a higher market capitalization and less in companies with a lower market capitalization.

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round off to the nearest hour 10 :54

Answers

Answer:

Step-by-step explanation:

the closest whole number on the hour is 11

Use the following equation to create a symbolic function Z: sin(/X+Y) X? +Y? (a) Use the finesh plotting function to create a three-dimensional plot of Z. (6) Use the fsurf plotting function to create a three-dimensional plot of Z. c) Use fcontour to create a contour map of Z. Use subplots to put all the graphs you create into the same figure.

Answers

To create various plots of the symbolic function Z, given by Z = sin(/X+Y) X? +Y?, we can use different plotting functions in MATLAB. The three-dimensional plot can be generated using the "plot3" function, the fsurf plotting function can be used to create a three-dimensional surface plot, and the fcontour function can be used to create a contour map of Z.

To create a three-dimensional plot of Z, we can use the "plot3" function in MATLAB, which allows us to plot in three dimensions. This plot will show the relationship between the variables X, Y, and Z.

For a three-dimensional surface plot, the "fsurf" function can be employed. This function will generate a surface plot that illustrates the behavior of Z in a more detailed manner.

To create a contour map of Z, the "fcontour" function can be utilized. This function will produce a two-dimensional plot with contour lines representing the values of Z.

By employing the "subplot" function in MATLAB, we can combine all the plots into a single figure, allowing for easy visualization and comparison.

The symbolic function Z can be visualized using the "plot3" function for a three-dimensional plot, the "fsurf" function for a three-dimensional surface plot, and the "fcontour" function for a contour map. By utilizing subplots, all the plots can be combined into a single figure.

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Comment on the stability of a system with the closed-loop transfer function given by each of the following

Answers

From the given information provided, the first system is stable while the second system is marginally stable.

To determine the stability of a system with a transfer function, we need to look at the poles of the transfer function, which are the roots of the denominator polynomial.

For the first transfer function, T(s) = 5 (s+2)/(s+1)(s² + s + 1), the denominator polynomial is s² + s + 1, which has complex conjugate roots with negative real part. Therefore, the system is stable.

For the second transfer function, T(s) = 5(-s+2)/(s+1)(s²+s+1), the denominator polynomial is s² + s + 1, which again has complex conjugate roots with negative real part. However, there is also a pole at s = -1, which is a real pole with negative real part. This means that the system is marginally stable, meaning that it is stable but any small perturbations or disturbances can cause the system to become unstable.

Question - Comment on the stability of a system with the closed-loop transfer function given by each of the following. T(s) = 5 (s+2)/(s+1)(s¹ + s+ 1) T(s)= 5(-s+2)/(s+1)(s¹+s+1)

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If x=2,find the value of x²+1/x²

Answers

Answer:

17/4 or 4 1/4

Step-by-step explanation:

Substitute x = 2 into the expression x² + 1/x².

(2)² + 1/(2)²

Evaluate the exponents in the expression.

(4) + 1/(4) 4 + 1/4

Multiply 4 by 4/4 to get a common denominator of 4.

16/4 + 1/4

Add the numerators together.

17/4

The value of x² + 1/x² if x = 2 is 17/4, or 4 1/4.

Prove by mathematical that for m1: 4+10+...+ (6m-2)= m (3+1) induction

Answers

We can prove by mathematical induction that for m₁: 4 + 10 + ... + (6m - 2) = m(3 + 1) holds true for all positive integers m.

To prove the given statement using mathematical induction, we need to show that it holds true for the base case (m = 1) and then prove the inductive step.

Base case:

When m = 1, the left-hand side of the equation becomes 4, and the right-hand side becomes 1(3 + 1) = 4. Thus, the equation holds true for the base case.

Inductive step:

Assume that the equation holds true for some positive integer k, i.e., 4 + 10 + ... + (6k - 2) = k(3 + 1).

We need to prove that the equation also holds true for k + 1, i.e., 4 + 10 + ... + (6(k + 1) - 2) = (k + 1)(3 + 1).

Starting with the left-hand side, we can expand it as follows:

4 + 10 + ... + (6(k + 1) - 2) = (4 + 10 + ... + (6k - 2)) + (6(k + 1) - 2).

Using our assumption for the sum up to 6k - 2, we can substitute k(3 + 1):

= k(3 + 1) + (6(k + 1) - 2).

Expanding the expression on the right-hand side, we get:

= 4k + 4 + 6k + 6 - 2.

Combining like terms, we have:

= 10k + 10.

Factoring out 10, we get:

= 10(k + 1).

This expression is equal to (k + 1)(3 + 1), which is the right-hand side of the equation.

Therefore, by mathematical induction, we have proved that for m₁: 4 + 10 + ... + (6m - 2) = m(3 + 1) holds true for all positive integers m.

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hello! Please may someone explain this question to me?

Answers

Answer:10°

Step-by-step explanation:

Triangle BDC is an isoceles triangle

180-30=150

150÷2=75

Then triangle ADC

75+30+65=170

180-170=10

Answer:

ΔBDC is isosceles, meaning the two base angles are equal. to find them you need to:

180 - 30 = 150 ÷ 2 = 75. so , each of the base angles is 75°

∠BDC + ∠BCD = ∠ABD

30 + 75 = 105°

so, x = 180 - (105+65) = 10°

you will understand better if you draw the figure and fill in all the angles following my explanation.

x = 10°

Enter the sum of numbers as a product of their GCF. 75 + 30 The sum of the numbers as a product of their GCF is

Answers

Answer: 75+30 = 15 x 7

Step-by-step explanation:

The given expression is 75+30 (=105) which defines the sum of 75 and 30.

Prime factorization of 75 and 30 are as below:

75 = 5 x 5 x 3

30 = 5 x 3 x 2

GCD (75,30) = 5x 3 = 15 [Note: GCD = Greatest common divisor]

Consider 75+30 = (15 x 5) + (15 x 2) [75 = 15 x 5 and 30= 15 x 2]

= 15 (5+2) [taking 15 as common ]

= 15 x (7)

(=105)

So, 75+30 which is sum of the numbers and it is expressed as 15 x 7 which a product of their GCF.

What is the value of y?

Answers

Answer:

umm i think it is 6.8 but i dontknow for sure

Answer:

y = 28

Step-by-step explanation:

GIVEN that,

AC = BC

Therefore, Angle A = Angle B

so, angle B = 32°

(Angles Opposite to equal sides are equal)

Using, Sum of all angles in a triangle = 180°

Angle A + Angle B + Angle C = 180°

34° + 34° + 4y = 180°

68° + 4y = 180°

4y = 180° - 68°

4y = 112°

y = 112/4

y = 28°

Hope it helps you!!

what is nine minus one third?

Answers

Answer:

$\frac{26}{3}$=$8.6...$=$8\frac{2}{3}$

Step-by-step explanation:

You multiply 9 x 3=27

(leave 1/3 alone, it's already good)

you have a 27/3-1/3

(subtract those)

your answer is 26/3

(see answer above for decimal form and mixed fraction form)

$\huge\sf\underline{Question}$
$\sf If \: {x}^{2} + \frac{1}{x ^{2} } = 34$
$\sf find \: the \: value \: of \: \: \: x + \frac{1}{x} $
a proper explanation needed :)

Thxx !!

Answers

$ {\qquad\quad\qquad\huge\underline{{\sf Answer}}} $

Here we go ~

$\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } = 34$

[ add 2 on both sides ]

$\qquad \sf \dashrightarrow \: {x}^{2} + \cfrac{1}{ {x}^{2} } + 2 = 34 + 2$

[ form identity : a² + b² + 2ab ]

$\qquad \sf \dashrightarrow \: {(x)}^{2} + { \bigg(\cfrac{1}{ {x}^{} } \bigg) }^{2} + 2 \sdot(x) \sdot \bigg(\cfrac{1}{x} \bigg) = 36$

[ a² + b² + 2ab = (a + b)² ]

$\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{2} = 36$

$\qquad \sf \dashrightarrow \: {\bigg (x + \cfrac{1}{x} \bigg) }^{} = \sqrt{ 36}$

$\qquad \sf \dashrightarrow \: x + \cfrac{1}{x} = \pm 6$

so, the value of required expression is 6

[usually positive value is considered, but if asked the value can be either positive or negative]

⚠️15 points⚠️ The table shows the linear relationship between the balance of a student's savings account and the number of weeks he has been saving. Based on the table, what was the rate of change of the balance of the student's savings account in dollars and cents per week?

Answers

Answer:

Where is the picture? I can help

Step-by-step explanation:

Answer:

Step-by-step explanation:

Solve for X
(3x – 47) (2X + 8)
O X= 56
O X= 55
O X= 59
O X = 45

Answers

Vertical angles are always congruent
Make an equation
3x - 47 = 2x + 8
3x = 2x + 55
Subtract 2x
x = 55

Solution: B. X = 55

Solve for X
(3x – 47) (2X + 8)
O X= 56
O X= 55. <————-
O X= 59
O X = 45

y = 3x + 8
8x + 4y = 12

Answers

Answer: good luck

Step-by-step explanation:Step 1) Because the first equation is already solved for

we can substitute

for

in the second equation and solve for

becomes:

(

)

(

⋅

)

(

⋅

)

(

)

−

Step 2) Substitute

−

for

in the first equation and calculate

becomes:

(

⋅

−

)

−

The solution is:

−

and

(

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)

The graph shows the population of a city from 1900 to 2000. What is the average rate of change of the population between 1950 and 1980?

Please help! I attached a photo of the graph.

Answers

Answer:

-15

Step-by-step explanation:

in 1950 it was 45 and in 1980 it was 30 so it is -15

The average rate of change can be define as the value of something is changing with respect to another thing is tinging. The average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

Given information-

The given graph shows the population of a city between the year 1900 to 2000.

Average rate of change-

The average rate of change can be define as the value of something is changing with respect to another thing is tinging.

Form the given graph,

The year 1950 is between the year 1940 and year 1960. The value at the y axis where the population (in thousand) shown is 45,000 for the year 1950.

The year 1980 is shown in graph at the x axis and the value of the population in the y axis is 30,000.

Thus the population is decreasing from year 1950 to 1980. The difference in the population of the year 1950 and 1980 is,

$d=45000-30000$

$d=15000$

Thus the change in the population between 1950 and 1980 is 15,000.

Average rate of change of the population between 1950 and 1980 -

As the population and the year both are changing. The rate of change for the population with respect to the year can be calculating by dividing the difference of the population between two year to the total years between the 1950 to 1980.

There is total 30 year from 1950 to 1980, thus the average rate of change is,

$A(x)=\dfrac{15000}{30} \\ A(x)=500$

Thus the average rate of change of the population between 1950 and 1980 is 500 per year. It means the population is decreasing with 500 per year.

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A statistics teacher notices a strong, negative, linear association between the number of missing assignments his students had and their report card grades. He computed a correlation coefficient of r=−0.9. Which of the following gives the correct value of the coefficient of determination, r2?

Answers

The coefficient of determination given the correlation coefficient is 0.81.

What is the coefficient of determination?

Correlation is used to measure the linear relationship between two variables. When the correlation coeffienient is negative, it means that the variables have a negative correlation. This means that the two variables move in opposite directions.

The coefficient of determination is used to measure the variation between the two variables being measured.

The coefficient of determination = correlation coeffienct²

-0.9² = 0.81

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need help fast !!!!!

Answers

Answer:

G(x) = 18

Step-by-step explanation:

first you add x on both sides (-7+x=11)

then you add 7 on both sides and end up with (x=18)

Tammy made $234 for 18 hours of work.
At the same rate, how many hours would she have to work to make $104?

Answers

Answer:

8 hours of work

Step-by-step explanation:

$234 ÷ 18 = $13 an hour

$104 ÷ 13 = 8 hours of work

The area of the triangle is 10 square units.
What is the measure of the base of the triangle?

Answers

Answer:

iwiwkkskskhsdvhsishvsuavuiisvys

Answer:

Step-by-step explanation:

I'm assuming that the triangle legs are the same length. if that's the case, set 10 equal to the triangle are formula.

A = 1/2 * b * h

10 = 1/2 * 2b (since both legs are same length assuming)

20 = 2b

b = 10 square units

Hope this helps

i give you 5 stars please help

Answers

Answer:

C....................

Answer:

Step-by-step explanation:

A line will be parallel to the y-axis if It’s x never changes.

In A, x is always being -y, so that’s going to change all the time.

In B, x is always becoming y, so that is changing too.

In C, x is always being 4, so this never changes.

In D, x is always 4 times y, so this changes.

Hope this helped!

what theorem is this
sss,sas,asa,aas,hl, or not enough info

Answers

ASA - verticals angles are equal, two sides are equal, and two other angles are marked equal

a data set consists of the data given below plus one more data point. when the additional point is included in the data set the sample mean of the resulting data set is 26.5. what is the value of the additional data point?23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19

Answers

The value of the additional data point is 36

To find the value of the additional data point, we can use the concept of the sample mean.

Given the data set: 23, 28, 20, 33, 42, 12, 19, 50, 36, 25, 19.

The sample mean of this data set is 26.5.

To find the value of the additional data point, we can use the formula for the sample mean:

(sample mean) = (sum of all data points) / (number of data points)

In this case, we have 11 data points in the original data set. Let's denote the value of the additional data point as x.

Therefore, we can set up the equation:

26.5 = (23 + 28 + 20 + 33 + 42 + 12 + 19 + 50 + 36 + 25 + 19 + x) / 12

Multiplying both sides of the equation by 12 to eliminate the fraction, we have:

318 = 282 + x

Subtracting 282 from both sides of the equation, we find:

x = 318 - 282

x = 36

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The table shows y as a function of x. Suppose a point is added to this table. Which choice gives a point that preserves the function?
Responses
A (−3, −8)(−3, −8)
B (−6, 3)(−6, 3)
C (−5, −2)(−5, −2)
D (9, 8)

Answers

The point that preserves the function is option A(-3,-8).

What do you mean by function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given question,

We have four option for the answer.

Note: if f is a function then each number of the domain has an unique image.

Since (regarding the table) the image of 9 is 6 then the answer D is wrong

The same apply on answers B and C .

Therefore, the right answer is A(-3,-8).

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What is the slope of the line that passes through the points (1, 6)(1,6) and (13, 2)(13,2)?

Answers

The slοpe οf the line passing thrοugh the pοints (1, 6) and (13, 2) is -1/3.

What is slοpe?

A line's slοpe, οften knοwn as its gradient, is a numerical representatiοn οf the line's steepness and directiοn.

Tο find the slοpe οf the line passing thrοugh the pοints (1, 6) and (13, 2), we can use the slοpe fοrmula:

slοpe = (y2 - y1) / (x2 - x1)

where (x1, y1) = (1, 6) and (x2, y2) = (13, 2).

Sο, the slοpe οf the line is:

slοpe = (2 - 6) / (13 - 1) = -4 / 12 = -1/3

Therefοre, the slοpe οf the line passing thrοugh the pοints (1, 6) and (13, 2) is -1/3.

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Find the highest common factor of 16,24 and 46

Answers

Answer:

The HCF would be 8 (1,2,4,8).

C. What part of the federal reserve’s congressional mandate does this scenario trigger (price stability and maximum sustainable employment

Answers

In the scenario you mentioned, the part of the Federal Reserve's congressional mandate that is triggered is both price stability and maximum sustainable employment.

The Federal Reserve has a dual mandate from Congress which consists of:

1. Price stability: This objective aims to maintain a stable inflation rate, ensuring that the purchasing power of money remains relatively constant over time. Price stability helps households and businesses make informed decisions regarding investments and consumption.

2. Maximum sustainable employment: This objective focuses on maintaining a high level of employment while avoiding unsustainable economic growth that could lead to high inflation. Achieving maximum sustainable employment involves minimizing unemployment while not causing inflation to rise significantly.

In the scenario you mentioned, the Federal Reserve would need to carefully balance its monetary policy to ensure that both objectives, price stability and maximum sustainable employment, are achieved. This might involve adjusting interest rates or using other monetary policy tools to influence economic activity, employment levels, and inflation.

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a bird flies from the bottom of a canyon that is 68 3/5 feet below sea level to a nest that is 676 3/5 feet above sea level. what is the difference in elevation between the bottom of the canyon and the birds nest

Answers

Answer: you can minus it

Step-by-step explanation:

676 3/5

-68 3/5

=606 0/0

the 0/0 can be left aswell

Please help is this a solution or inequality 5-x<8;x=-3

Answers

Answer:

Its a inequality

Step-by-step explanation:

YOUR WELCOME LOVE YOU

This is an inequality. Refer to the char below.

The two expressions we have is ‘5 - x’ and ‘8’. If X is equal to three, then we get ‘5 - 3’ and ‘8’. This comes out to 2 > 8.

Hope this helps :)

Please help is this a solution or inequality 5-x<8;x=-3

before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. true false

Answers

True, Logarithms were used extensively for complicated calculations before the electronic calculator became widely available. A logarithm is a mathematical function that helps simplify complex arithmetic operations by converting multiplication and division into addition and subtraction, respectively.

By using logarithms, complex calculations could be broken down into simpler steps and performed more easily. Logarithms were particularly useful in fields such as astronomy, physics, and engineering, where large numbers and complicated formulas were common. However, with the advent of electronic calculators, the use of logarithms for everyday calculations declined. Today, logarithms are still used in certain fields and for specific applications, but they are no longer the primary tool for carrying out complicated calculations.

Before the electronic calculator became widely available, logarithms were used to carry out complicated calculations. Logarithms simplified complex calculations by turning multiplication and division operations into addition and subtraction.

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