1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alinara [238K]
3 years ago
13

Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series expansion. Do not show that

Rn(x) → 0.] f(x) = 8x − 3x3, a = −2 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 28(x + 2) + 18(x + 2)2 − 3(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 28(x + 2) + 3(x + 2)2 − 18(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 + 28(x + 2) + 18(x + 2)2 + 3(x + 2)3 [infinity] f n(−2) n! (x + 2)n n = 0 = 8 − 18(x + 2) + 28(x + 2)2 − 3(x + 2)3
Mathematics
1 answer:
kherson [118]3 years ago
5 0

Answer:

The answer is

f(x) = {\displaystyle  8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }

Step-by-step explanation:

Remember that Taylor says that

f(x) = {\displaystyle \sum\limits_{k=0}^{\infty} \frac{f^{(k)}(a) }{k!}(x-a)^k }

For this case

f^{(0)} (-2) = 8(-2)-3(-2)^3 = 8\\f^{(1)} (-2) = 8-3(3)(-2)^2 = -28\\f^{(2)} (-2) = -3(3)2(-2) = -36\\f^{(2)} (-2) = -3(3)2 = -18

f(x) = {\displaystyle  8 + \frac{-28}{1}(x+2)+\frac{-36}{2!}(x+2)^2 + \frac{-18}{3!}(x+2)^2 }

You might be interested in
Marsha jogged 7.8 miles. erica jogged 0.5 times as far. how far did erica jog?
wolverine [178]
Solve:-

7.8 × 0.5 = How far Erica jogged
7.8 × 0.5 = 3.9
3.9 Miles

So, if Marsha jogged 7.8 miles, and Erica jogged 0.5 times as far, as Marsha, Erica jogged 3.9 Miles.

Hope I helped ya!! xD
6 0
2 years ago
A music club has 35 drum players. If 25% of the total number of members in the club are drum players, what is the total number o
Pachacha [2.7K]

Answer:

140

Step-by-step explanation:

Since 25% is 1/4 of 100, that means that 35 is 1/4 of the total amount of members in the club. So, 35 times 4 is 140.

3 0
3 years ago
Use multiples to write two fractions equivalent to 9/10
pochemuha
18/20 and 27/30 hope this helps
8 0
2 years ago
Read 2 more answers
Is 18.4 rational or irrational ?
DaniilM [7]

Answer:

It is Rational.

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
PLZ HELP, AND PLZ EXPLAIN
shutvik [7]

Answer:

C

Step-by-step explanation:

To make it easy let's start by organizing our information :

  • AC=12 AND BD=8
  • ABCD is a rhombus
  • K and L are the midpoints of sides AD and CD
  • we notice that the rhombus ABCD is divided into four right triangles

What do you think of when you hear a right triangle ?

  • The pythagorian theorem !

AC and BD  are khown so let's focus on them .

If we concentrated we can notice that AB and BD are cossing each other in the midpoints . why ?

Simply because they are the diagonals of a rhombus .

ow let's apply the pythagorian theorem :

  • (AC/2)² + (BD/2)² = BC²
  • 6²+4²=52
  • BC²= 52⇒\sqrt{52}=BC

Now we khow that : AB=BC=CD=AD=\sqrt{52}

This isn't enough . Let's try to figure out a way to calculate the length of KL  wich is the base of the triangle

  • KL is parallel to AC
  • k is the midpoint of AD and L of DC

I smell something . yes! Thales theorem

  • KL/AC=DL/DC=DK/AD WE4LL TAKE OLY ONE
  • KL/12=\sqrt{52}/2*\sqrt{52}  
  • KL/12=1/2⇒ KL=6

Now we have the length of the base kl

Now the big boss the height :

  • notice that you khow the length of KL
  • BD crosses kl from its midpoint and DL = \sqrt{52} /2

What I want to do is to apply the pythgorian thaorem to khow the lenght of that small part that is not a part of the height of the triangle . I will call it D

  • DL²=(KL/2)²+D²
  • 52/4= 9+ D²
  • D² = 52/4-9 +4 SO D=2

now the height of the trigle is H= BD-D= 8-2=6

NOw the area of the triangle is :

  • A=(KL*H)/2 ⇒ A= (6*6)/2=18

THE ANSWER IS 18 SQ.UN

5 0
3 years ago
Other questions:
  • A circle has a radius of 3. Which is the closest approximation to the area of the circle?
    9·1 answer
  • Farmer Ed has 600 meters of fencing
    11·1 answer
  • Weights of women in one age group are normally distributed with a standard deviation σ of 18 lb. A researcher wishes to estimate
    5·1 answer
  • Please help me with this surds question. Explain how you got your answer.
    8·1 answer
  • Jane ran 72 miles in 6 days. Then she tripled her rate. How long would it take her to travel 648 miles at the new speed?
    9·1 answer
  • HELP PLEASE!! Please don't give me sites or links, those won't work since the site is blocked
    8·1 answer
  • Does this equation have:
    12·1 answer
  • Please help me to find this answer
    5·1 answer
  • M
    7·2 answers
  • 30 POINTS PICTURE ADDED | What is the equation of this graphed line?
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!