Find a power series representation for the function. (Give your power series representation centered at x=0 .) f(x)=15+x

Answers

Answer 1

Answer:

[tex]f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}[/tex]

Step-by-step explanation:

Given

[tex]f(x) = \frac{1}{5 + x}[/tex]

Required

The power series centered at [tex]x = 0[/tex]

We have:

[tex]f(x) = \frac{1}{5 + x}[/tex]

Factor out 5 from the denominator

[tex]f(x) = \frac{1}{5(1 + \frac{x}{5})}[/tex]

Rewrite as:

[tex]f(x) = \frac{\frac{1}{5}}{(1 + \frac{x}{5})}[/tex]

Further, rewrite as:

[tex]f(x) = \frac{1}{5}(1 + \frac{x}{5})^{-1}[/tex]

Expand the bracket

[tex]f(x) = \frac{1}{5}(1 - \frac{x}{5} + (\frac{x}{5})^2 - (\frac{x}{5})^3+..........)[/tex]

Evaluate all exponents

[tex]f(x) = \frac{1}{5}(1 - \frac{x}{5} + \frac{x^2}{25} - \frac{x^3}{125}+......)[/tex]

Open brackets

[tex]f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......[/tex]

Notice the pattern as:

[tex]f(x) = \frac{1}{5} - \frac{x}{5^2} + \frac{x^2}{5^3} - \frac{x^3}{5^4}+......\± \frac{x^n}{5^{n+1}}[/tex]

So, the power series is:

[tex]f(x) = \sum\limits^{\infty}_{n=0} \frac{-(1)^n\cdot x^n}{5^{n+1}}[/tex]


Related Questions

How would yo expand ln (1/49k)?

Answers

Answer:

Step-by-step explanation:

It depends on whether you mean ln(1/49k) or ln(1/(49k)).

A researcher surveyed 8 people to see if there is a
relationship between years of education and starting
salaries. The data points are shown on the graph.
Which best represents the equation of the trend line
shown on the graph? (Note that the graph has a break
on the x-axis.)
O y = 0.25x + 15
O y = 0.25x + 17.5
* y = 1.25x - 10
O y = 1.25x + 7.5

Answers

Answer:

[tex]y=1.25x+7.5[/tex]

Step-by-step explanation:

We can see that the trend line is the line of best fit to the data points.

The equation of a straight line is given by:

y = mx + b:

where y, x are variables, m is the slope of the line and b is the y intercept.

From the graph, we can see that the line passes through the points (10, 20) and (14, 25). Therefore the equation of the line is given by:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-20=\frac{25-20}{14-10}(x-10)\\\\y-20=1.25(x -10)\\\\y-20=1.25x-12.5\\\\y=1.25x+7.5[/tex]

five times a number minus two is ten .find the number

Answers

Answer:

12/5 or 2.4

Step-by-step explanation:

Form the equation:

5x - 2 = 10

^     ^     ^

^     ^    "is ten" which adds a equal sign to it

^   minus two

five times a number  

Solve:

5x - 2 = 10

     +2    +2

-----------------

5x = 12

----   ----

5      5

x = 12/5 or 2.4

Let the number be x

Then ATQ

5x - 2 = 10

5x = 10+2

x = 12/5

Must click thanks and mark brainliest

4. In SI, motor output is rated in
A. horsepower.
B. newtons.
C.foot-pounds per second.
D. kilowatts.

Answers

Answer:

in so in Newton motor out put is rate

***URGENT*** PLEASE HELP ME ASAP, ITS DUE TODAY!!!

...................................

M is the midpoint of 0A. N is the midpoint of OB. Prove that AB is parallel to MN​

Answers

Answer:

Construct MN.

Since M is the midpoint of OA, OM = MA

Similarly, N is the midpoint of OB.

Thus, ON = NB.

Now, in Δs OMN and OAB,

∠MON = ∠AOB (common angle)

(sides are in proportional ratio; OA = 2OM and OB = 2ON)

∴ Δs OMN and OAB are similar (2 sides are in proportion, with the included angle)

Since they are similar, then ∠OMN = ∠OAB (corresponding angles of similar triangles are equal)

But since ∠OMN = ∠OAB, then that means MN || AB (corresponding angles of two lines must be equal since they also sit relative to the transverse line, OA)

Thus, AB || MN (QED)

A random sample of 64 students at a university showed an average age of 25 years and a sample standard deviation of 2 years. The 98% confidence interval for the true average age of all students in the university is

Answers

Answer:

24.4185<x<25.5815

Step-by-step explanation:

Given the following:

n = 64

mean x = 25

s = 2

z is the z score at 98% CI = 2.326

Get the Confidence Interval:

CI = x±z*s/√n

CI = 25±2.326*2/√64

CI = 25±2.326*2/8

CI = 25±0.5815

CI = (25-0.5815, 25+0.5815)

CI = (24.4185, 25.5815)

CI = 24.4185<x<25.5815

Hence the 98% confidence interval for the true average age of all students in the university is 24.4185<x<25.5815

this khan academy problem confuses me... (5/3)^3= can anyone help me solve it?

Answers

Answer:

4.629

Step-by-step explanation:

(5/3)³5×5×5/3×3×3125/274.629.

Hope it is helpful to you

Riley wants to make 100ml of 25% saline but only has access to 12% and 38% saline mixtures. x= 12% y=38%

Answers

Answer:

x = 50

y = 50

Step-by-step explanation:

[tex]\begin{bmatrix}x+y=100\\ 0.12x+0.38y=25\end{bmatrix}[/tex]

.12(100-y) + .38y = 25

x = 50

y = 50

What is circulatry systerm​

Answers

Answer: i think you meant circulatory system but the defination for it is:

The  circulatory system (also called the cardiovascular system) is the body system that moves blood around the body. It consists of the heart and blood vessels. The blood carries various materials that the body needs, and takes away waste or harmful substances. Blood vessels that take blood away from the heart are arteries.

Which expression is equivalent to 9+y+y+3

Answers

Answer:

b

Step-by-step explanation:

You only need to add the real numbers and the ys.

Answer:

12 + 2y

Step-by-step explanation:

9+y+y+3

Combine like terms

9+3   + y+y

12 + 2y

Solve the equation
P=100x-0.1x^2

Answers

Answer:

100x - 0.01x

Step-by-step explanation:

100x-0.1x^2

100x - 0.01x

The admissions officer at a small college compares the scores on the Scholastic Aptitude Test (SAT) for the school's in-state and out-of-state applicants. A random sample of 10 in-state applicants results in a SAT scoring mean of 1173 with a standard deviation of 38. A random sample of 15 out-of-state applicants results in a SAT scoring mean of 1076 with a standard deviation of 57. Using this data, find the 95% confidence interval for the true mean difference between the scoring mean for in-state applicants and out-of-state applicants. Assume that the population variances are not equal and that the two populations are normally distributed. Find the margin of error to be used in constructing the confidence interva.

Answers

Answer:

jebtucky

Step-by-step explanation:

yes yee yee yee eyetegevw

which of the following is not an asymptote of the hyperbola xy = -42? y = 0 x = 0 y = x

Answers

Given:

The equation of the hyperbola is:

[tex]xy=-42[/tex]

To find:

The the equation which is not an asymptote of the hyperbola.

Solution:

We have,

[tex]xy=-42[/tex]

It can be written as:

[tex]y=\dfrac{-42}{x}[/tex]

Equating denominator and 0, we get

[tex]x=0[/tex]

So, the vertical asymptotic is [tex]x=0[/tex].

The degree of numerator is 0 and the degree of denominator is 1.

Since the degree of numerator is greater that the degree of denominator, therefore the horizontal asymptote is [tex]y=0[/tex] and there is no oblique asymptote.

Therefore, [tex]y=x[/tex] is not an asymptote of the given hyperbola and the correct option is C.

Find the area and perimeter of a rectangle with length measuring 14 cm and width measuring 5 more than twice the length.

Answers

Answer:

AREA: 462cm

PERIMETER: 94cm

Step-by-step explanation:

To find the width, you have to double 14 and then add 5. That would equal 33. Then to find area, multiply 33 and 14 = 462. To find perimeter, add 33+33+14+14=94

The area of the rectangle is 462 cm² and the perimeter is 94 cm.

How to determine the  area and perimeter

To find the area and perimeter of a rectangle, we need the length and width of the rectangle.

Given:

Length = 14 cm

Width = 2(14) + 5

Calculating the width:

Width = 2(14) + 5

Width = 28 + 5

Width = 33 cm

Now, we can calculate the area and perimeter of the rectangle.

Area of a rectangle:

Area = Length x Width

Substituting the values:

Area = 14 cm x 33 cm

Area = 462 cm²

Perimeter of a rectangle:

Perimeter = 2(Length + Width)

Substituting the values:

Perimeter = 2(14 cm + 33 cm)

Perimeter = 2(47 cm)

Perimeter = 94 cm

Therefore, the area of the rectangle is 462 cm² and the perimeter is 94 cm.

Learn more about area and perimeter at

https://brainly.com/question/19819849

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Which of the following statements are true?

A. Both graphs are exponential functions.
B. Both graphs are logarithmic functions.
C. Both graphs have exactly one asymptote.
D. Both graphs have been shifted and flipped.

Answers

Answer:

A, C, and D are the answers to this question

The true statements about the graphs are; A. Both graphs are exponential functions. C. Both graphs have exactly one asymptote. D. Both graphs have been shifted and flipped.

How to Interpret Function Graphs?

The graphs are exponential functions because as x increases, the value of y approaches infinity.

Likewise the graphs have exactly one asymptote.

Lastly, we can see that both graphs appear to have been shifted and flipped especially when we look at their respective coordinates.

Read more about Function Graphs at; https://brainly.com/question/11507546

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The stem-and-leaf plot above shows house sale prices over the last week in Tacoma. What was the most
expensive house sold? Give your answer in dollars
$

Answers

Answer:

the answer is 2

Step-by-step explanation:

29 and one-fifth divided by 4 and StartFraction 6 over 7 EndFraction

Answers

Answer:

6 1/85

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

146/5÷34/7

Applying the fractions formula for division,

146/5*7/34=1022/170

Simplifying 1022/170, the answer is

6 1/85

Bill invested $4000 at 6%
compounded annually. Find the
accumulated amount at the end of
12 years.

Answers

Answer:

$ 8048.79

Step-by-step explanation:

P = $4000t = 12 yearsr = 6% = 0.06

Formula:

A = P(1 + r)^t

The total amount:

A = 4000*(1 + 0.06)^12 = 8048.79

We have to find the,

Accumulated amount at end of 12 years.

The formula we use,

→ A = P(1+r)^t

It is given that,

→ P = $4000

→ t = 12 years

Then r will be,

→ 6%

→ 6/100

→ 0.06

Then the total amount is,

→ P(1+r)^t

→ 4000 × (1 + 0.06)^12

→ 8048.79

Thus, $ 8048.79 is the amount.

The quadratic equation [tex]x^2+3x+50 = 0[/tex] has roots r and s. Find a quadratic question whose roots are r^2 and s^2.

Answers

According to the question, our quadratic equation is :

\begin{gathered} \bf {x}^{2} - ( {r}^{2} + {s}^{2} )x + {r}^{2} {s}^{2} = 0 \\ \bf \implies \: {x}^{2} - ( - 91)x + {(rs)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + {(50)}^{2} = 0 \\ \bf \implies \: {x}^{2} + 91x + 2500 = 0\end{gathered}

x

2

−(r

2

+s

2

)x+r

2

s

2

=0

⟹x

2

−(−91)x+(rs)

2

=0

⟹x

2

+91x+(50)

2

=0

⟹x

2

+91x+2500=0

Hshejoffpeowhwbwbwhjskfofofoekwwoksnfnf Helppp

Answers

Answer:

Step-by-step explanation:

3. ZW ≅ WX

use the function to find f(-2) f(x)=[tex]3^{x}[/tex]

Answers

Answer:

[tex] \frac{1}{9} [/tex]

Step-by-step explanation:

[tex]f( - 2) = {3}^{ - 2} [/tex]

[tex]1 \div 9 = .111[/tex]

After the booster club sold 40 hotdogs at a football game, it had $90 in profit.
After the next game, it had sold a total of 80 hotdogs and had a total of $210
profit. Which equation models the total profit, y, based on the number of
hotdogs sold, X?

Answers

Step-by-step explanation:

x = goods y = $

x Sold = 40, Y = $90

x Sold = 80, Y = $210

sum of xHotdogs = 40+80 = 120 Hotdogs

Sum of Y$ = $90 + 210 = 300

so

X = 2A & Y = 3 its mean one hotdogs can sold for one each = $2.25 and we round it to $3

So = XY = 2A + 3

sorry if i wrong

write your answer in simplest radical form​

Answers

Step-by-step explanation:

5ft hight this ancle 90°so

answer is 5ft

Ethan buys a video game on sale. If the video game usually costs $60, and it was on sale for 20% off, how much did Ethan pay? Round to the nearest whole dollar.

Answers

Ethan will pay $31.99 with the discount.

How? This is the answer because:

If 39.99 is 100%, and you are trying to find 20%...

1. you need to set it up as a ratio (of course, you do not need to do this, but it is easier for me to do it this way)

2. the ratio will look like this: 39.99/100% x/20%

3. all we need to do from here is to cross multiply!

4 39.99 x

---------- = ----------

100 20

-price is on the top and percent on the bottom

-you would now do 39.99 times 20

-then divide by 100

5. once you have 20% of 39.99, you need to subtract that answer from the total

6. 39.99 - 7.998 = 31.992 (you need to round to the nearest hundredth)

Hope this helps <3

Two real estate companies, Century 21 and RE/MAX, compete with one another in a local market. The manager of the Century 21 office would like to advertise that homes listed with RE/MAX average more than 10 days on the market when compared to homes listed with his company. The following data shows the sample size and average number of days on the market for the two companies along with the population standard deviations.Sample mean Sample size Population standard deviation Century 21 22 days 36 32 days RE/MAX 144 days 30 35 daysIf Population 1 is defined as RE/MAX and Population 2 is defined as Century 21, the 80% confidence interval for the difference in population means is:_________.(17.8, 26.2)(11.5, 32.7)(5.4, 38.6)(-3.0, 47.0)

Answers

Answer:

17.8 , 26.2

Step-by-step explanation:

The confidence interval is 80% for the given population. Significance level is 0.2 [ 1 - 0.8 ] . Sample size is given and sample mean is calculated with the given standard deviation. Sample mean is 36 days and population size is 144 days.

If a right circular cone is intersected by a plane only at its vertex, as in the
picture below, what shape is produced?
A. A parabola
B. An ellipse
C. A point
D. A line
E. A circle
F. A hyperbola

Answers

Answer:

A point

Step-by-step explanation:

Hopefully this helps :)

If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.

What is mean by cone?

A cone is a three-dimensional geometric form with a flat base and a smooth, tapering apex or vertex. A cone is made up of a collection of line segments, half-lines, or lines that link the base's points to the apex, which is a common point on a plane that does not include the base.

Now, If a right circular cone is intersected by a plane passing through its vertex and perpendicular to its base, the resulting shape is a point.

Since, This is because a plane passing through the vertex of a cone and perpendicular to its base intersects the cone at only one point, which is the vertex of the cone.

Alternatively, if the plane intersects the base of the cone at any other point than the center, the resulting shape would be a triangle.

Therefore, the required form is a point.

Learn more about the cone visit:

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Complete the sentence that explains why Write an Equation is a reasonable strategy for solving this problem. Because the answer may be _________ the numbers in the problem.

Answers

Answer:

4 e

Step-by-step explanation:

dz6dxrx xrrx6 xz33x4xr4x xrx

13) What is 4 1/2 subtracted from 5.33?
A. 0.43
B. 0.53
C. 0.83
D. 1.08

Answers

Given:

[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33.

To find:

The value for the given statement.

Solution:

[tex]4\dfrac{1}{2}[/tex] subtracted from 5.33 can be written as:

[tex]5.33-4\dfrac{1}{2}[/tex]

On simplification, we get

[tex]=5.33-\dfrac{8+1}{2}[/tex]

[tex]=5.33-\dfrac{9}{2}[/tex]

[tex]=5.33-4.5[/tex]

[tex]=0.83[/tex]

Therefore, the correct option is C.

help help me please!!!!!!!​

Answers

9514 1404 393

Answer:

  a) 3092.5 (rounded to tenths)

  b) 39,600

  c) ₹28,755

Step-by-step explanation:

These are all simple calculator problems. The arithmetic involved is something you learned in 2nd or 3rd grade.

__

a) Since we divide using the division algorithm, it isn't clear what "check your answer by division algorithm" is intended to mean. The result of the division (stopping at 1 decimal place) is 3092.5.

The usual method of checking a division problem is to multiply the quotient by the divisor to see if the dividend value is the result. Here, we have ...

  13×3092.5 = 40202.5

This differs by from the dividend of 40203 by 0.5, which is the remainder showing in our long division. In short, the answer checks OK.

__

b) The value of each 4 is found by setting other digits to 0.

  Most significant 4: 40,000

  Least significant 4: 400

Difference in place value: 40,000 -400 = 39,600

__

c) The balance in the account is found by subtracting withdrawals from deposits:

  ₹35000 -6245 = ₹28,755

 

Which point is the vertex for the graph of y = |x| + 2?
A. (0,1)
B. (0,-2)
C. (0,2)
D. (2,0)

Answers

Answer:(0,2) is the vertex for the graph of y = |x| + 2.

Step-by-step explanation:  |x| = 0, y + 2 = 2

Therefore, It would be ( 0,2)

Answer:

trust the otherguy

Step-by-step explanation:

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