Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x) centered at the given value of a. (Enter your answers as a comma-separated list.) f(x) = 7xex, a = 0

Answers

Answer 1

Answer:

The four first terms are:

[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]

Step-by-step explanation:

The function is:

[tex]f(x)=7xe^{x}[/tex]

The Taylor series around a is given by:

[tex]F(x)=\sum^{\infty}_{n=0} \frac{f^{n}(a)(x-a)^{n}}{n!}[/tex]

The first 4 terms will be:

[tex]F(x)=f(0)+\frac{f^{'}(0)(x)}{1}+\frac{f^{''}(0)(x)^{2}}{2}+\frac{f^{'''}(0)(x)^{3}}{6}[/tex]  

Let's find first the derivatives:

[tex]f'(x)=7(xe^{x}+e^{x})[/tex]

[tex]f'(0)=7(0e^{0}+e^{0})=7[/tex]

[tex]f''(x)=7xe^{x}+7e^{x}+7e^{x}=7xe^{x}+14e^{x}[/tex]  

[tex]f''(0)=14[/tex]  

[tex]f'''(0)=21[/tex]

[tex]f''''(0)=28[/tex]    

[tex]F(x)=0+\frac{7(x)}{1}+\frac{14(x)^{2}}{2}+\frac{21(x)^{3}}{6}+\frac{28(x)^{4}}{24}[/tex]

Therefore, the four first terms are:

[tex]7x,7x^{2},\frac{21x^{3}}{6},\frac{7x^{4}}{6}[/tex]

I hope it helps you!

 

   

Answer 2

So the Taylor series for the function informed will be:

[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]

The function is:

[tex]f(x)= 7e^xx[/tex]

The Taylor series around a is given by:

[tex]f(x)= \sum \frac{f^n (a) (x-a)^n }{n!}[/tex]

The first four terms will be:

[tex]F(x)=f(0)+\frac{f'(0)(x)}{1}+\frac{f''(0)(x)^2}{2} + \frac{f'''(0)(x)^3}{6}[/tex]

Let's find first the derivaties:

[tex]f'(x)= 7(e^xx+e^x)\\f'(0)= 7\\f''(x)= 7e^xx+14e^xx\\f''(0)=14\\f'''(0)= 21\\f''''(0)= 28[/tex]

[tex]F(x)= 0+\frac{7x}{1}+\frac{14x^2}{2}+\frac{21x^3}{6}+\frac{28x^4}{24}[/tex]

Therefore, the four first terms are:

[tex]7x; 7x^2; \frac{21x^3}{6} ; \frac{7x^4}{6}[/tex]

See more about Taylor series at : brainly.com/question/6953942


Related Questions

These cones are similar. Find the surface
area of the smaller cone. Round to the
nearest tenth.
2 cm
3 cm
Surface Area = [ ? ) cm2 Surface Area = 75 cm2
Helppppp plssss

Answers

Answer:

33.3 cm²

Step-by-step explanation:

Recall: Area Scale Factor = (Linear Scale Factor)²

Area scale factor = surface area of bigger cone/surface area of smaller cone

Let the surface area of the smaller cone be represented as x

Therefore,

Area scale factor = 75/x

Linear scale factor = radius of bigger cone/radius of smaller cone = 3/2

Thus:

75/x = (3/2)²

75/x = 9/4

Cross multiply

x*9 = 75*4

9x = 300

Divide both sides by 9

x = 300/9

x = 33.3 cm² (nearest tenth)

Find the measure of 0. Round answer to the nearest tenth. Pleas help

Answers

Answer:

[tex]\theta=36.43^{\circ}[/tex]

Step-by-step explanation:

Given that,

Base = 42

Perpendicular height = 31

We need to find the value of [tex]\theta[/tex]. It can be calculated using trigonometry as follows :

[tex]\tan\theta=\dfrac{P}{B}\\\\\theta=\tan^{-1}(\dfrac{P}{B})[/tex]

Put all the values,

[tex]\theta=\tan^{-1}(\dfrac{31}{42})\\\\\theta=36.43^{\circ}[/tex]

So, the value of [tex]\theta=36.43^{\circ}[/tex].

A soccer team has 15 players and needs to choose a captain and an assistant captain. How many ways can those positions be selected?
Select one:

105

50

30

Answers

Answer:

30?

Step-by-step explanation:

I think its 30 because 15*2 is 30 but I really don't know im sorry

Please answer number 5 I’ll give brainliest thanks

Answers

Answer:

Hello! answer: C

Hope that helps!

Answer:

b

Step-by-step explanation:

Experimental - 5 choices, 1 is Q = 1/5

Theoretical - 5 choices, landed on Q 4 times =4/5

Five times the sum of 4 and some number is 40.

Answers

Answer:

5 × 4 = 20 not 40

Step-by-step explanation:

Which inequality can be used to represent this scenario?
Mikael needs to rent a scooter to get to work. The scooter charges $1.85 to activate it and $0.50 per mile Mikael has a gift card for
$10 and he can not spend more on the scooter
O 10 < 0.502 +1.85
O 10 < 1.85.1 +0.50
O 10 > 1.852 +0.50
O 10 > 0.503 +1.85

Answers

Answer:

[tex]10 > 1.85 + 0.5m[/tex]

Step-by-step explanation:

Price of the scooter:

Fixed price of $1.85 to activate plus $0.50 for each mile. This situation can be represented by a linear function, and it is given by:

[tex]P(m) = 1.85 + 0.5m[/tex]

Mikael has a gift card for $10 and he can not spend more on the scooter.

The spendings have to be less than 10. So

[tex]10 > P(m)[/tex]

[tex]10 > 1.85 + 0.5m[/tex]

A system of equations is created by using the line represented by2x+4y=0And the line represented by the data in the table below
What is the X value of the solution to the system if x -1 and y is 8

Answers

Answer:

x = 2

Step-by-step explanation:

From the data, we obtain the slope :

-1, 8 ; 3, - 4

Slope = Rise / run

Rise = y2 - y1 = (-4 - 8) = - 12

Run = x2 - x1 = (3 - (-1)) = 4

Slope, m = - 12 / 4 = - 3

Recall:

Equation of line :

y - y1 = m(x - x1)

y - 8 = - 3(x + 1)

y - 8 = - 3x - 3

y = - 3x - 3 + 8

y = - 3x + 5

Substituting y = - 3x + 5 into the equation 2x+4y= 0

2x + 4(-3x + 5) = 0

2x - 12x + 20 = 0

-10x = - 20

x = 2

brainliest eeeeeeeeeeeeee

Answers

Answer:

3 / 4

Step-by-step explanation:

We can realize that both the numerator and denominator have a common factor of 9. We can divide them both by 9 to get:

3 / 4

This fraction is in simplest form.

Answer:

3/4

hope this helps

have a good day :)

Step-by-step explanation:

what is the volume of the cube I'm confused (look at the picture to see) ​

Answers

Answer: D (64)

Step-by-step explanation:

My answer is correct because, it's showing that 4 is the length, width, and height. So it bassically 4 x 4 x 4 in other words 4 exponent 3. And 4 exponent 3 would equal 64.

Hope This Helps!

Connor made 16 brownies. He put nuts on 6 brownies. Write
the simplified fraction of the brownies that had nuts.

Answers

6/16 = 3/8

hope this helps

graph your linear equation. y=x÷3​

Answers

here ya go
(correct me if wrong)

When there are 24 cars in the parking lot, the lot is ⅜ full. What is the maximum capacity (total number of cars) that the parking lot can hold? Show your work.

not really tricky just a little thing I needed help with

Answers

Answer:

64 cars

Step-by-step explanation:

total number of cars that the parking lot can hold = 8/3 × 24 = 64 cars

Help pls!

(The question are in the image)
A. -1/p
B. 0
C. 1
D. p

Answers

It would probably be C
C I’m pretty sure lol

PLssssssssssssss help..

Answers

Answer:

141.4

Step-by-step explanation:

i think

solve the given system of equations 2x + 8y= 5 and 24x - 4y = -15

Answers

9514 1404 393

Answer:

  (x, y) = (-1/2, 3/4)

Step-by-step explanation:

A graphing calculator does a nice job of finding the solution.

  (x, y) = (-1/2, 3/4)

__

You can eliminate y by adding twice the second equation to the first.

  (2x +8y) +2(24x -4y) = (5) +2(-15)

  50x = -25

  x = -1/2 . . . . . . divide by 50

__

  24(-1/2) -4y = -15 . . . . .substitute for x in the second equation

  -4y = -3 . . . . . . . . . add 12

  y = 3/4 . . . . . . . . . divide by the coefficient of y

The solution is (x, y) = (-1/2, 3/4).

Rodas is standing 100 feet from the Eiffel Tower and sees a bird land on the top of the tower (he has really good eyes!). If the angle of elevation from Rodas to the top of the Eiffel Tower is close to 84.6°, how tall is the tower? Round to two decimal places.

Answers

Answer:

1057.89 feet

Step-by-step explanation:

Trig time! Start with a diagram and listing out your trig functions, either mentally or on paper. SOH CAH TOA

The best trig function for this problem is likely tan:

tan84.6 = height / 100

100 * tan 84.6 = height

height = 1057.89 feet


Pllssss somebody help me fast pllls!!!

Answers

Answer:

Yes; That what I got In my studies and lessons

Yes.



Hope it helped:)

These marbles are placed in a bag and two
of them are randomly drawn.
What is the probability of drawing two yellow
marbles if the first one is NOT placed back into
the bag before the second draw?
Give your answer as a rational number, reduced to
simplest terms.
1
[ ?
Hint: Multiply the probability of the 1st Event by the
probability of the 2nd Event to get your answer.

Answers

Answer: 1/45

Step-by-step explanation:

If a vertical angle has 74 degree and also opposite angle is 2x degree ,what is value of x?​

Answers

Answer:

x = 37

Step-by-step explanation:

Well if you didn't know vertical angles are congruent ( or equal to each other )

Which means that 74 = 2x

If we want to find the value of x, then we need to get rid of the "2" on 2x

To do so we can divide each side by 2

74 / 2 = 37

2x / 2 = x

we would be left with x = 37

Emma buys two bus tickets to Bradford. She pays with a £10 note. How much change will she get?

Answers

Hello there I hop you are having a good day :)

So, if she brought 2 tickets an they cost £4.00 you would add £4.00 + £4.00 = £8.00 and then you would take that away from the £10.00 - £8.00 = £2.00 so Emma would get £2.00 change :) hopefully that helps you.

What the guy on top of me said ^

Mandy and Jordan each bought some of the same notebook and the same three-ring
binder. Mandy paid $11.20 for 2 notebooks and 2 binders. Jordan paid $10.50 for 3
notebooks and 1 binder. What is the price of one of the notebooks?

Answers

Answer:

$11.20 + 2 = 1122  1050 +3 = 1053 hope this help .

What are the vertices of AA'B'C'if AABC is dilated by a scale factor of 5?

Answers

Answer:

B

Step-by-step explanation:

multiply each coordinate by 5

solve if h=5 and y=8 7hy^2+y

Answers

Step-by-step explanation:

h = 5

y = 8

=> 7hy² + y

=> 7 × 5 × 8² + 8

=> 35 × 64 + 8

=> 2240 + 8

=> 2248

5 pennies as a fraction​

Answers

Answer:

5/100

Step-by-step explanation:

each penny = 1/100

If using the method of completing the square to solve the quadratic equation x² - 16x - 38 = 0, which number would have to be added to "complete the square"?

Answers

Answer:64

Step-by-Step

Image

You roll 2 dice. What is the probability of getting two 5's?

Answers

The coment before me is super funny lol
The heck burger burger burger burger burger burger

A multiple choice test contains questions


with four options each: A, B, C, or D. If


Natalie randomly guesses on the last three


questions, what is the probability that she


gets all three correct?

Answers

Answer:

Probability of getting all three correct answer =  [tex]\frac{1}{64}[/tex]

Step-by-step explanation:

Given - A multiple choice test contains questions  with four options each: A, B, C, or D. If  Natalie randomly guesses on the last three  questions.

To find - what is the probability that she  gets all three correct.

Proof -

Given that,  question has 4 options.

And 1 option can be correct,

Let

x be that Natalie gives correct answer.

So,

Probability of getting, correct answer, P(x) = [tex]\frac{1}{4}[/tex]

So,

Probability of getting, incorrect answer, P(x') = 1 -  [tex]\frac{1}{4}[/tex] = [tex]\frac{3}{4}[/tex]

Now,

Given that, she guess the 3 questions.

All correct means,

first, second, third question answer is correct.

So,

Probability of getting all three correct answer = [tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex]×[tex]\frac{1}{4}[/tex] = [tex]\frac{1}{64}[/tex]

Please I need help badly please no links or I will report you

Answers

Answer:

17.5 is going to be your answer

help me plzzzzzz!!!!!!!​

Answers

42 i think i may be wrong

Help pls. No links. Thank you :)

Answers

Answer:

784

Step-by-step explanation:

Mark as Brainliest

P.S

other person is wrong

Other Questions
please help me with this. will give brainliest due in 5 minutes Which equations is parallel to y=4x+8? a simple act of kindness will help me answer thisI WILL MAKE YOU BRAINLIEST Write an equation for the proportional relationship shown in the table 7m + 3mnwhen m = 3 and n = -4 HELP pleaseYoungest to oldest n more than 12A) n/12B) 12 +nC) 22D) 12-n Find the length of c using the Pythagorean theorem Which sentence is most clearly a theme?O A. A little hope is all it takes to overcome great challenges.B. The king exits. The queen enters, followed by servants.O c. A cat and a dog form an unlikely friendship on a farm.O D. The clouds floated like suds on the surface of a bath.NEED ASAP !! How long will it take $10,000 to double at 11% simple interest? (Round to the nearest year) Chloe breaks into the pantry after Albert goes to work. She finds and opens a family-pack of mixed nuts. After surfing the web, she finds that these packs claim to be 20% almond (A), 30% cashew (C), 10% macadamia (M), and 40% peanut. Chloe discovers that her bag contains 14 almonds, 28 cashews, 6 macadamias, and 52 peanuts. a) Perform an appropriate test to determine whether this claim is true or not at a = 0.05. State all the relevant steps (listed in exercise 1). b) What is the decision and conclusion (write a sentence) at a = 0.1? c) Chloe is a choosy and sneaky doggie. She likes to find a p-value first and then come up with a significance level, a later so she can reject as many Hos as possible. Is her method acceptable? Write a poem that expresses a wish or a dream of yours. What is the range of the function f(x)=2x+4f(x)=2x+4 when the domain is {-2, 0, 3}?A. {0, 4, 10}B. {4.25, 5, 12}C. {4.25, 4, 12}D. All real numbers who was the founder of ghori rule A school eacher took some student to the amusement park. 1/2 of them has 3 rides on the merry-go-round. 3/5 of the remainder had two rides and the rest of the children had one ride. If 8 students had one ride. How many students did she take to the amusement park? I need help on this equation Wait what about this one The product of -3 and -7 is positive.True False Im very confused help, please "Any time anyone makes a comic book into a movie, in some way, i think they have to kill the comic book" Anybody knows what this means?? Its a quote. plzzz help me. no links tho