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]
2 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]2 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
two people were doing yard work for 1 hour and 35 minutes then they stopped for lunch at 1:20pm at what time did they start doin
MrMuchimi

Answer: The answer would be at 11:45.

Step-by-step explanation: First I though, if they stoppedd for lunch at 1:20 and they've been doing yard work for 1 hour and 35 minutes, I would subtract. 1 hour taken away from 1:20 would be 12:20. Then, since it would be hard to subtract 35 minutes from 12:20, 35 minutes - 20 minutes = 15 minutes. 12:20 subtract 20 minutes = 12:00. 12:00 - 15 minutes equal to 11:45. I hope this helps. I know this explanation can be confusing but it's the best I can do at the moment.

<h3 />
4 0
3 years ago
Alex bought 9 2/3 pounds of hamburger meat for a cookout. He plans to make 1/3 pound hamburgers.What is the maximum number of 1/
sladkih [1.3K]
29 you divide 1/3 by 9 and add the extra 2
8 0
3 years ago
Read 2 more answers
Malia owns 1 out of 3 gas stations in Jasper. In Webster, Abby owns 6/25 of the gas stations. Who owns a greater fraction of gas
Katarina [22]

Answer:

I think it would be Malia but if I'm wrong please let me know.

3 0
2 years ago
HELP PLEASE. 3(2x+3)=15​
pantera1 [17]

If you are  solving for X then we have to do a few process

What you would want most is to remove the parentheses, so to do that i would use distributive property

3*2x is 6x and 3*3 is 9  so our new equation will look like

6x+9=15 if you don't understand please tell me

now we must bring the 9 over

If you bring the 9 over than it would become negative

6x=15-9

so 6x=6

and now you can solve the answer is x=1

7 0
1 year ago
Read 2 more answers
Using the chart below, determine which option would be the cheapest overall? Option Number of Months Down Payment Interest Rate
Gekata [30.6K]

Answer:

Answer:

Option 1, by $851.70

Step-by-step explanation:

Option 1 total:

$8000 + $765.44*5*12 = $53926.40

Option 2 total:

$8000 + $626.25*4*12 + 0.38*$43995 = $54778.10

The difference:

$54778.1 - $53926.40 = $851.70

As we see the option 1 is cheaper by $851.70

Correct answer choice is the last one

Step-by-step explanation:

8 0
2 years ago
Other questions:
  • 7- a. What is the radius of the circle with center (3,10) that passes through (12,12)?
    13·1 answer
  • A rocket took off at a speed of 7.9 kilometers per second. How many miles per hour does the rocket travel if 1 km is 0.62 miles?
    14·1 answer
  • 2/3(6y+9)<br> Need help
    15·2 answers
  • Find the surface area of the composite solid.
    7·1 answer
  • I NEED HELP WITH 4 PROBLEMS PLEASE HELP ME QUICKLY! 1.-6(1+7k)+7(1+6k) is less than or equal to -2 2. -2(2-2x)-4(x+5) is less th
    5·1 answer
  • How do I solve equation 24=2a + 6
    5·1 answer
  • Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 5.15 ft at
    8·1 answer
  • Read the story. Barry is on the school tennis team. At practice yesterday, he did 3 forehand strokes for every 2 backhand stroke
    8·1 answer
  • Help please I don’t understand this and help me with any question you want thank you!:((
    13·1 answer
  • Jack is at the zoo looking up at a monkey
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!