Use a Maclaurin series in the table below to obtain the Maclaurin series for the given function f(x) = 2ex + e6x n=0 TABLE 1 | l = Sx" = 1 + x + x2 + x3 + . Important Maclaurin Series and Their Radii of Convergence R 1 no n! 2n+1 otsin x = n=0(-1)" (2n + 1).-x-31+51-71 R=0 0 2n+1 R 1 -0ntl k(k-1) (1+x)" = (k)x" = 1 +kx + k(k-1)(k-2) , x3 + , R=1

Answers

Answer 1

The  radius of convergence for the Maclaurin series of f(x) is R = 1.

To obtain the Maclaurin series for the given function f(x) = 2ex + e6x, we can use the Maclaurin series expansions of the exponential function. The Maclaurin series for ex is given by e^x = Σ(x^n/n!) from n=0 to infinity, with a radius of convergence of R = ∞.

Using this, we can rewrite the given function as f(x) = 2e^x + e^6x. Substituting the Maclaurin series expansion of ex into the first term and the Maclaurin series expansion of e^6x into the second term, we get:

f(x) = 2(Σ(x^n/n!)) + (Σ((6x)^n/n!))
= 2Σ(x^n/n!) + Σ((6^n)(x^n)/n!)

Now we can combine the two series by collecting like terms and coefficients. The resulting Maclaurin series for f(x) is:

f(x) = Σ((2/n! + (6^n)/n!)(x^n))

The radius of convergence of this series will be determined by the smaller of the radii of convergence of the individual series used, which is R = 1 for the series of ex and R = 1 for the series of e^6x. Therefore, the radius of convergence for the Maclaurin series of f(x) is R = 1.

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Related Questions

Given a ≠ ± b and (a^2-b^2) / (a+b)=12 find a-b.
(I will give brainliest for helpful answers. Please don't put a link in the answer box.)

Answers

Answer:

[tex] \sqrt{12a \: + \: 12b \: - \: 2ab \: + \: 2b {}^{2} } [/tex]

Step-by-step explanation:

(a²-b²) / (a+b) = 12

a² - b² = 12(a+b)

(a-b)² + 2ab - 2b² = 12a + 12b

(a-b)² = 12a + 12b - 2ab + 2b²

a - b =

[tex] \sqrt{12a \: + 12b \: - 2ab \: + \: 2b {}^{2} } [/tex]

Question is in picture

Answers

Answer:

The answer is 32 inches

65 - 33 = 32

32 inches 728-928 for 32 inches

What Is The Difference Between Apparent Capacity And Actual Capacity Of A Glass Vessel? IN SURFACE AREA AND VOLUME!!​?​

Answers

The apparent capacity of a glass vessel refers to its perceived size or volume based on external dimensions, while the actual capacity represents the true volume of the vessel, taking into account both interior and exterior dimensions.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

PLEASE HELP ME, I HAVE BEEN WAITING FOR A DAAYY!! How old am i if 400 reduced by 3 times my age is 244?

Answers

Answer:

52 years

Step-by-step explanation:

Let

Your age = x

3 times your age = 3 * x

= 3x

The equation can be written as:

400 - 3x = 244

400 - 244 = 3x

156 = 3x

Divide both sides by 3

x = 156/3

x = 52

Therefore,

Your age is 52 years

please help me yall, Godbless.

Answers

Answer:

The rate of change or slope is 2

Step-by-step explanation:

Rise over run 2/1

Can someone help me with this. Thank you.

Answers

Answer:

All are true

Step-by-step explanation:

2) True

3) True

4) True

All the answers are true

what ratio is equivalent to 2/1

Answers

Answer:12 : 6 22 : 11 32 : 16

Step-by-step explanation:

Answer:

4:2

Step-by-step explanation:

PLZ HELP ASAP WILL MARK BRAINLIEST

Answers

Answer:

72[tex]\sqrt{3}[/tex]

Step-by-step explanation:

The area (A) of a rhombus is calculated as

A = [tex]\frac{1}{2}[/tex] × d₁ × d₂ (d₁ and d₂ are the diagonals )

The diagonals bisect each other at right angles

d₁ = 2 × 6 = 12

Use the tangent ration in the upper left right triangle and the exact value

tan60° = [tex]\sqrt{3}[/tex]

tan60° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{opp}{6}[/tex] = [tex]\sqrt{3}[/tex] ( multiply both sides by 6 )

opp = 6[tex]\sqrt{3}[/tex] , then

d₂ = 2 × 6[tex]\sqrt{3}[/tex] = 12[tex]\sqrt{3}[/tex]

Thus

A = [tex]\frac{1}{2}[/tex] × 12 × 12[tex]\sqrt{3}[/tex] = 6 × 12[tex]\sqrt{3}[/tex] = 72[tex]\sqrt{3}[/tex]

Which of the following statistical information about the data is calculated by the Column Statistics tool? Select the two correct answers ,Threshold calculation,Date analysis,Regression analysis,Median calculation

Answers

The correct answer is: Median calculation and Threshold calculation.

Median calculation: The Column Statistics tool can calculate the median of a dataset. The median is the middle value in a sorted dataset. It is a measure of central tendency that divides the data into two equal halves. Calculating the median can provide insights into the central value of a dataset and is less sensitive to extreme values compared to other measures like the mean.

Threshold calculation: The Column Statistics tool can calculate thresholds or cutoff points based on the data. These thresholds define certain conditions or ranges in the data. For example, you can set a threshold to identify data points above a certain value as outliers or flag data points that fall within a specific range. Threshold calculations can be useful for data cleansing, anomaly detection, or creating categorical variables based on certain conditions.

The other options, Date analysis and Regression analysis, are not typically calculated by the Column Statistics tool. Date analysis involves examining patterns and trends related to dates or time, which may require specialized techniques such as time series analysis or date-specific functions. Regression analysis is a statistical technique used to model the relationship between variables and requires more advanced tools or methods beyond basic column statistics.

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Find (f+g)(x).

f(x) = 1
-
x

g(x) = x^2 + 2x-5

Answers

Answer:

(f + g)(x) = x² + x - 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Terms/CoefficientsFunctionsFunction Notation

Step-by-step explanation:

Step 1: Define

f(x) = 1 - x

g(x) = x² + 2x - 5

(f + g)(x) is f(x) + g(x)

Step 2: Solve

Substitute in functions:                                                                                     (f + g)(x) = (1 - x) + (x² + 2x - 5)Combine like terms (x):                                                                                    (f + g)(x) = x² + x - 5 + 1Combine like terms:                                                                                         (f + g)(x) = x² + x - 4

what is the answer someone help me!!!

Answers

Answer:

14.4in so your radius is your third answer

find the area of the rectangle PLUM khan academy

Answers

Answer:

Length x Breadth

Step-by-step explanation:

can u help pls like pls

Answers

Answer:

E. 16

Step-by-step explanation:

Easy:

Formula: P=2(l+w)

Plug in and solve:

P=2(3+5)

P = 16 (Option E is correct)

The answer is option E 16cm

Write the first four terms of the sequence{an}defined by the following recurrence relation.
an+1=2a2n-1;a1=0

Answers

The first 4-terms of sequence {aₙ} defined by recurrence-relation : aₙ₊₁ = 2aₙ²-1;  a₁ = 0 are 0, -1, 1 and 1.

To find the first four terms of the sequence {aₙ} defined by the recurrence relation aₙ₊₁ = 2aₙ² - 1, with the initial-condition a₁ = 0, we apply the recurrence relation,

Starting with a₁ = 0, we can find the subsequent terms as follows:

⇒ a₂ = 2a₁² - 1 = 2(0)² - 1 = -1

⇒ a₃ = 2a₂² - 1 = 2(-1)² - 1 = 1

⇒ a₄ = 2a₃² - 1 = 2(1)² - 1 = 1

Therefore, the first four terms of the sequence are : a₁ = 0, a₂ = -1, a₃ = 1

and a₄ = 1.

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The given question is incomplete, the complete question is

Write the first four terms of the sequence {aₙ} defined by the following recurrence relation.

aₙ₊₁ = 2aₙ²-1;  a₁ = 0.

phoebe compared the cost of books in 9 different stores. $2, $8, $4, $7, $8, $5, $8, $4, $6 what is the median cost of the books?

Answers

The median cost of the books is $6.

To find the median, we first arrange the costs of the books in ascending order: $2, $4, $4, $5, $6, $7, $8, $8, $8. Next, we determine the middle value. Since there are nine values, the middle value is the fifth one, which is $6. Therefore, the median cost of the books is $6.

The median is a statistical measure that represents the middle value of a dataset when it is arranged in ascending or descending order. It is useful in situations where there are outliers or extreme values that could skew the average. By using the median, we can get a better representation of the typical value in the dataset.

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Find the equation for the
following parabola.
Focus (3, 4)
Directrix y = 2
A. (x-3)2 = 2(y-2.5)
B. (x-3)2 = 4(y-3)
C. (x-3)2 = (y-4)
D. (y-3)2 = 4(x-3)

Answers

Option A is correct.The equation for the parabola is A.(x - 3)^2 = 2(y - 2.5)

The equation for a parabola with a focus (h, k) and a directrix y = a can be expressed as:

(x - h)^2 = 4a(y - k)

The focus is (3, 4) and the directrix is y = 2, we can substitute these values into the equation:

(x - 3)^2 = 4(2)(y - 4)

Simplifying:

(x - 3)^2 = 8(y - 4)

The correct equation for the parabola is:

(x - 3)^2 = 8(y - 4)

Therefore, the answer is option A. (x - 3)^2 = 2(y - 2.5)

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Oliver just accepted a job at a new company where he will make an annual salary of
$54000. Oliver was told that for each year he stays with the company, he will be
given a salary raise of $3000. How much would Oliver make as a salary after 6 years
working for the company? What would be his salary after t years?

Answers

Answer:

After 6 Years:  54000*6 + 3000*5 = 339,000

After t years: 54000*t + 3000*(t-1) = 57000 t - 3000

==============

Please give brainliest, I really want to rank up, thank you!

Answer:

$358,000

Step-by-step explanation:

He makes $54k dollars "annual" = per year

Each year he stays he gets $3k worth of a raise

He stays 6 years so

3000 x 6 = 18k

54,000 x 6= 340,000

so then you just add

18,000 + 340,000=

358,000

I hope that helps :D

Ahh i hate math fr someone help

Answers

i think C but probably try to find something to back it up
All you gotta do is divide the pound by the cost

Gavin is subdividing land into two plots, where one plot is in the shape of a square and the other plot is in the shape of a rectangle. The square plot of land has a side length of 6x3 feet, and the rectangular plot of land has a length of 3x5 feet and a width of 7x2 feet. Use the properties of exponents to determine the expression that represents the area for each plot of land. Then analyze which plot of land has a larger area if x is 3.

Answers

You have to multiply both of those

Find the smallest sample size needed to estimate the percentage of Americans who prefer to watch the news rather than read or listen to it. Use a 0.03 margin of error and a confidence level of 99%. From a previous poll, it was found that 47% of the American respondents prefer to watch the news rather than read or listen to it.

Answers

To estimate the percentage of Americans who prefer to watch the news rather than read or listen to it with a 0.03 margin of error and 99% confidence level, the smallest sample size needed is 1,060.

To calculate the sample size, we can use the formula:

n = (Z² * p * (1 - p)) / E²

where:

n = sample size

Z = Z-score corresponding to the desired confidence level (in this case, for a 99% confidence level, Z ≈ 2.576)

p = estimated proportion of the population with the characteristic of interest (based on the previous poll, p = 0.47)

E = margin of error (E = 0.03)

Substituting the values into the formula, we have:

n = (2.576² * 0.47 * (1 - 0.47)) / 0.03²

n ≈ 1060

Therefore, the smallest sample size needed to estimate the percentage of Americans who prefer to watch the news rather than read or listen to it, with a 0.03 margin of error and 99% confidence level, is approximately 1,060. This means that a sample of at least 1,060 individuals should be surveyed to obtain reliable estimates with the desired level of confidence.

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PLEASE HELP FAST NEED IT FAST =)


Which pair of triangles demonstrates congruence with the AAS Postulate?

Answers

Answer:

B

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

brainliest?

ONLY ANSWER IF U KNOW!
Find the limit of the function algebraically.

Answers

Answer:

lim [(x(2) + 3) × 1/ x(4) ] = 3 × ( + ○○) = + ○○

PLEASE HELPP!!!!
The wingspan of a hawk is the distance from the end of one spread-out wing to the end of the other spread-out wing. A scientist measured the wingspans of a random sample of hawks at a national park. Based on the median wingspan of the sample, the scientist estimates that the median wingspan of all hawks in the national park is 40 inches. Which graph most likely represents the data from the scientist's sample?

Answers

Answer:

D)

Step-by-step explanation:

It looks like the most sense

find x
answer choices
6
7
9
10
8

Answers

The answer should be 10

you are part of a group of tourists in Yosemite National Park who want to rent bikes to ride around the valley floor. you arrive at the bicycle rental shop and see that there are two different rental plans:

Plan A: $15 initial fee, plus $2 per hour
Plan B: $5 initial fee, plus $4 per hour

The group doesn't know which plan is best for each person, but you volunteer to use your algebra skills to analyze the situation. Define two variables, write and solve a system of equations to answer the following questions.

a) For which people is plan A best? For which people is plan B best?

b) When are the costs of the two plans the same and what is the cost?

Answers

Answer:

a

Step-by-step explanation:

A is the correct answer

Type a digit that makes this sentence true!

Answers

Answer:

1

best answer ever be amazing

Adjustment for Merchandise Inventory Using T Accounts: Periodic Inventory System

Ibby Smith owns and operates Ibby’s Ice Cream Cones. Her beginning inventory as of January 1, 20--, was $45,000, and her ending inventory as of December 31, 20--, was $57,000. Set up T accounts for Merchandise Inventory and Income Summary and perform the year-end adjustment for Merchandise Inventory.

Use the labels shown.

(a) Remove the beginning balance in Merchandise Inventory.
(b) Add the new balance in Merchandise Inventory.

Answers

The Income Summary will be credited for $12,000 in the T account.

The journal entry to remove the beginning balance in Merchandise Inventory is as follows:
Merchandise Inventory Debit $45,000
Opening Inventory Credit $45,000
In the T account of Merchandise Inventory, the beginning balance of $45,000 will be subtracted from the total of the debit amounts in the account.

ii. Add the new balance to Merchandise Inventory

The journal entry to add the new balance to Merchandise Inventory is as follows:
Closing Inventory Debit $57,000
Merchandise Inventory Credit $57,000
In the T account of Merchandise Inventory, the ending balance of $57,000 will be added to the total of the credit amounts in the account.

The year-end adjustment entry for Merchandise Inventory is:

Merchandise Inventory Dr. $57,000 ($57,000 - $45,000)
Income Summary Cr. $57,000 ($57,000 - $45,000)
In the Merchandise Inventory T account, the ending balance is $12,000 (credit balance) since the credit amount of $57,000 exceeded the debit amount of $45,000 by $12,000.
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B
39 m
Use the inverse trigonometric keys
on a calculator to find the measure
of angle A.
А
21 m
с
A=
(Round the answer to the nearest whole number.)

Answers

Answer:

the answer is 20 because you round of 21

In a lab, Andrew is studying the growth of a particular species of bacteria. The bacteria in the petri dish started at 300. After 2 days he realizes that the number of bacteria is about 480. After another 2 days he realizes that the number of bacteria in the dish is 288 more than what it was two days ago. a.) Give an equation to estimate the amount of bacteria in the dish after every day. b.) At what rate would the bacteria be growing c.) How many days would it take for the bacteria to reach almost 1229. d.) Find the average rate of change between 6 days and the first day

Answers

a) The equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.

b) The coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.

c) It would take approximately 11.32 days for the bacteria to reach almost 1229.

d) Average rate of change = (N₂ - 300) / (6 - 1)

a) Let's denote the number of bacteria in the dish after a certain number of days as N. We can create an equation to estimate the amount of bacteria in the dish after every day based on the given information.

On the first day, the initial number of bacteria is 300. After 2 days, the number of bacteria is approximately 480. This gives us two data points: (1, 300) and (3, 480).

To find the equation for estimating the number of bacteria, we can use the two-point form of the linear equation:

N - 300 = ((480 - 300) / (3 - 1))(t - 1)

Simplifying the equation, we get:

N = 90t + 210

Therefore, the equation to estimate the amount of bacteria in the dish after every day is N = 90t + 210.

b) The rate at which the bacteria is growing can be determined from the coefficient of t in the equation. In this case, the coefficient is 90, indicating that the bacteria is growing at a rate of 90 per day.

c) We can use the equation N = 90t + 210 to find the number of days it would take for the bacteria to reach almost 1229. We substitute N = 1229 into the equation and solve for t:

1229 = 90t + 210

1019 = 90t

t ≈ 11.32

Therefore, it would take approximately 11.32 days for the bacteria to reach almost 1229.

d) To find the average rate of change between 6 days and the first day, we need to calculate the change in the number of bacteria divided by the change in time:

Average rate of change = (N₂ - N₁) / (t₂ - t₁)

Here, N₁ is the number of bacteria on the first day (300), t₁ is the first day (1), N₂ is the number of bacteria on the sixth day, and t₂ is the sixth day.

Substituting the values into the formula, we get:

Average rate of change = (N₂ - 300) / (6 - 1)

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Write an expression that can be used to find the length of JH and an expression that can be used to find the length of GJ.​

Answers

Answer: JH = 9 sin(35)

not sure about GH...

Step-by-step explanation:

The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.

The expression required to fine the length of GJ is,

[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]

The length of the [tex]GJ[/tex] is 5.162 units.

What is right angle triangle?

A right angle triangle is the triangle in which measure of one of the angle is equal to the 90 degrees.

The ratio of opposite side of the triangle hypotenuse side of triangle is equal to sine of angle.

Given information-

In the given triangle shown in the figure,

[tex]\angle JGH=35[/tex]

The angle [tex]\angle HJG[/tex] is right angle, which is equal to the 90 degrees.

As the sum of all the angles of a triangle is equal to the 180 degrees. Thus,

[tex]\angle JGH+\angle HJG+\angle GHJ=180\\[/tex]

Put the values,

[tex]35+90+\angle GHJ=180\\125+\angle GHJ=180\\\angle GHJ=180-125\\\angle GHJ=55[/tex]

In the given triangle, the side [tex]GJ[/tex] is the opposite side of the triangle and [tex]GH[/tex] is the hypotenuse side of the triangle.

Thus the length of the [tex]GJ[/tex] for the right triangle can be given as,

[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]

This is the required expression,

[tex]GJ=\sin 35\times9\\GJ=0.574\times9\\GJ=5.162[/tex]

Thus the length of the [tex]GJ[/tex]5.162 units.

The expression required to fine the length of GJ is,

[tex]\sin 35=\dfrac{GJ}{9}\\[/tex]

The length of the [tex]GJ[/tex]5.162 units.

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