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
Viefleur [7K]
3 years ago
10

Find a power series representation for the function. (Give your power series representation centered at x = 0.) f(x) = x/6x^2 +

1 f(x) = sigma^infinity_n = 0 (-1)^n x^2n+1 6^n Determine the interval of convergence. (Enter your answer using interval notation.)
Mathematics
1 answer:
timama [110]3 years ago
3 0

Looks like your function is

f(x)=\dfrac x{6x^2+1}

Rewrite it as

f(x)=\dfrac x{1-(-6x^2)}

Recall that for |x|, we have

\dfrac1{1-x}=\displaystyle\sum_{n=0}^\infty x^n

If we replace x with -6x^2, we get

f(x)=\displaystyle x\sum_{n=0}^\infty\frac(-6x^2)^n=\sum_{n=0}^\infty (-6)^n x^{2n+1}

By the ratio test, the series converges if

\displaystyle\lim_{n\to\infty}\left|\frac{(-6)^{n+1} x^{2(n+1)+1}}{(-6)^n x^{2n+1}}\right|=6|x^2|\lim_{n\to\infty}1=6|x|^2

Solving for x gives the interval of convergence,

|x|^2

We can confirm that the interval is open by checking for convergence at the endpoints; we'd find that the resulting series diverge.

You might be interested in
Which of the following side lengths can form a triangle?
Margaret [11]

Okay, so my last answer was deleted because I didnt show any work.


According to the rule,


a+b>c

c+b>a

c+a>b


so...


2+3=6...6<7

21+23=44...44+44

12+36=48...48<53

14+17=31...31>30


Since answer D is the only answer that fullfills the rule a+b>c, it is the correct answer


3 0
3 years ago
Read 2 more answers
Help please soon !!!!!!
stepan [7]
75.25x + 3604 = 300.50x
300.50x - 75.25x = 3604
225.25x = 3604
x = 16
Both companies charged the same at 16 tons
first answer 16 tons
--------------------
300.50x = 300.50(16) = $4,808
both companies charged the same are $4,808
second answer is $4,808
5 0
3 years ago
The figure shows a square and 4 congruent isosceles triangles. If the length of leg x is 12 feet, what is the length in feet of
allsm [11]

Answer:

wher eis the

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
What is the area?Please i need help
antiseptic1488 [7]

Answer:

65

Step-by-step explanation:

Base by High

then divided by 2

4 0
3 years ago
The shaded area of the picture shows what part of the yard Rashon mowed in 15 minutes. He wonders how long it will take him to m
irina [24]

Answer:60

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Write the point-slope form of the line that passes through (1, -5) and is parallel to a line with a slope of 1. Include all of y
    6·2 answers
  • Simplify the following: 3t^2 t (4t w) 8tw w^2
    9·1 answer
  • A ball is thrown in the air from a ledge. Its height in feet is represented by f(x) = –16(x2 – 7x – 8), where x is the number of
    10·2 answers
  • Find the distance between (− 3, 10) and (5, 22)
    10·1 answer
  • What is the area of this figure?<br><br> A. 102<br> B. 132<br> C. 168<br> D. 340
    13·1 answer
  • A parabola can be drawn given a focus of (-4, -5) and a directrix of y=3. Write the equation of the parabola in any form.
    6·1 answer
  • Un estudiante obtuvo las siguientes calificacion 5,7_6,2_4,6 obteniendo un promedio 5 calificaciones¿que nota obtuvo en la ultim
    12·1 answer
  • Let f(x) = 3x and g(x) = x2 + 1. Find g(f(x))
    7·2 answers
  • I need help making a proof for geometry! Here is the question I really need help on this question my marking period ends soon!
    5·1 answer
  • Please help!!!! Find the value of x.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!