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
Igoryamba
3 years ago
5

Find a power series for the function, centered at c. 7x c=0 x2+5x 6 , g(x) - Determine the interval of convergence. (Enter your

answer using interval notation.)
Mathematics
1 answer:
babunello [35]3 years ago
4 0

Answer:

\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }

and the interval of the convergence is (-1, 1)

Step-by-step explanation:

To find a power series for the function, centered at c.

g(x) = \dfrac{7x}{x^2 +5x-6} ,\ c = 0

If we factorize the denominator, we have:

g(x) = \dfrac{7x}{(x +6)(x-1)}

g(x)= \dfrac{1}{x-1}+\dfrac{6}{x+6}

Thus;

g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1+\dfrac{x}{6}}

g(x)= \dfrac{-1}{1-x}+\dfrac{1}{1-(-\dfrac{x}{6})}

g(x) = - \sum \limits^{\infty}_{n=0} x^n + \sum \limits^{\infty}_{n=0} x^n(\dfrac{-x}{6})^n \  \ if \  \ |x| < 1 \  \ and \ \  |\dfrac{x}{6}< 1

g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n , \ if |x|

\mathbf{g(x) = \sum \limits^{\infty}_{n=0} (-1 + (\dfrac{-1}{6})^n)x^n }

and the interval of the convergence is (-1, 1)

You might be interested in
Help please i need it thanks.
Shalnov [3]

Answer:

x is less than or equal to 7

Step-by-step explanation:

8 0
2 years ago
A zoo has 2 male lions one sixth oh the lions are male lions how many lions are there at the zoo ?
Deffense [45]
I'm guessing there are 12 lions since half of twelve is 6 and there is only 2 male lions. I would put down 12. Hope that helps!
8 0
4 years ago
Read 2 more answers
In a society there are 30 men and 20 women members.
krek1111 [17]
<h3>Answer:  2/5</h3>

This is because there are 20 women out of 50 people total (30+20 = 50).

So 20/50 = 2/5

This converts to the decimal form 0.4 and the percentage form 40%

3 0
3 years ago
I need the answer for this question.
Grace [21]
If the whole angle (ABC) is equal to 133, we can add angles ABD and DBC to find x.

10x+13=133
Subtract 13 from both sides to get
10x=120
Divide both sides by 10 to get that x=12

We can now plug the value of x into ABD to find its measure.
7(12)+4
Simplifies to 84+4, which is 88

So angle ABD is equal to 88 degrees.

:)
8 0
3 years ago
In a certain sequence of numbers, each term after the first is found by doubling and then adding $3$ to the previous term. If th
eimsori [14]
Given a_7=125 you can find a_6:

a_6= \frac{125-3}{2} =61
 a_5= \frac{61-3}{2} =29 \\ a_4= \frac{29-3}{2}=13 \\ a_3= \frac{13-3}{2} =5 \\ a_2= \frac{5-3}{2} =1 \\ a_1= \frac{1-3}{2}=-1
Answer: -1
6 0
3 years ago
Other questions:
  • The measure of an angle is 111°. What is the measure of a supplementary angle?
    9·1 answer
  • How do you graph an explict equation
    9·1 answer
  • If sales tax is 7.75%, what is the total cost of an 11$ purchase including tax?
    13·2 answers
  • I will mark u brainleiest if u help me and 5 stars
    10·2 answers
  • Melodys family wants to go to Hawaii, which is a 3,700 mile airplane ride. Write the number of miles in scientific notation
    14·1 answer
  • The line contains the point (3, 2) and is parallel to a line with a slope of -3.
    7·1 answer
  • Write the function for each graph below.​
    14·1 answer
  • Is (-2, 0) the solution to the system below?
    6·2 answers
  • Pls help, math work!!!
    9·2 answers
  • Find an equation for the line with slope m= -2/3
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!