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
babunello [35]
3 years ago
9

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) = 10 x , a = −2
Mathematics
1 answer:
Helga [31]3 years ago
4 0

Answer:

\sum^\infty_{n=0} -5 (\frac{x+2}{2})^n

Step-by-step explanation:

Rn(x) →0

f(x) = 10/x

a = -2

Taylor series for the function <em>f </em>at the number a is:

f(x) =  \sum^\infty_{n=0} \frac{f^{(n)}(a)}{n!} (x - a)^n

f(x) = f(a) + \frac{f'(a)}{1!}(x-a)+\frac{f"(a)}{2!} (x-a)^2 + ... ............ equation (1)

Now we will find the function <em>f </em> and all derivatives of the function <em>f</em> at a = -2

f(x) = 10/x            f(-2) = 10/-2

f'(x) = -10/x²         f'(-2) = -10/(-2)²

f"(x) = -10.2/x³      f"(-2) = -10.2/(-2)³

f"'(x) = -10.2.3/x⁴     f'"(-2) = -10.2.3/(-2)⁴

f""(x) = -10.2.3.4/x⁵    f""(-2) = -10.2.3.4/(-2)⁵

∴ The Taylor series for the function <em>f</em> at a = -4 means that we substitute the value of each function into equation (1)

So, we get \sum^\infty_{n=0} - \frac{10(x+2)^n}{2^{n+1}} Or \sum^\infty_{n=0} -5 (\frac{x+2}{2})^n

You might be interested in
How many 1/4 pound packages of cheese can the deli make with 12 pounds of cheese
SSSSS [86.1K]

Answer:

48 1/4 packages

Step-by-step explanation:

8 0
2 years ago
What is the maximum value of the picture below?
Cloud [144]

Answer:

y = 4

Step-by-step explanation:

The maximum value occurs at the vertex

vertex = (2, 4 )

when x = 2 the maximum value is y = 4

4 0
2 years ago
a town's population is currently 5,500.if the population doubles every 91 years, what will the population be 182 years from now​
Blizzard [7]

Answer:

I think the answer is 22,000

7 0
3 years ago
Read 2 more answers
ANSWER TO BE NAMED BRAINLIEST GET A THANK YOU BE FRIEND REQUESTED AND GET 5 STAR VOTE PLEASEEE HELP I AM REALLY STUCK
Anon25 [30]

Answer:

17

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
50 points! Can you please be honest and answer these 3 questions.
Zepler [3.9K]

Answer:

1. 5/10

2. 0.54

3. √3 and -1/16????

I think

sorry if I wrong

3 0
2 years ago
Other questions:
  • Which product of prime polynomials is equivalent to 8x4 + 36x3 – 72x2?
    9·2 answers
  • What is 92 83/125 in simplest form, but still as a mixed number?
    14·1 answer
  • How do u find the area of a regular polygon? And can someone help me with question 2
    7·1 answer
  • What does VII-IX mean?
    13·1 answer
  • What is the mean absolute deviation of the data set? Use paper and pencil,
    11·1 answer
  • Please help!! Brainiest answerWorth 15 points
    12·1 answer
  • Solve <br> 4x+3y=-2<br> 3x + 5y = 15
    14·1 answer
  • Which triangles are right triangles?<br> Select ALL correct answers.
    12·1 answer
  • Brainliest for correct answer, any inapplicable answer or absurd answer will be deleted and reported.
    6·1 answer
  • This is due in a bit and im having a bit of trouble, any solutions?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!