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
topjm [15]
3 years ago
6

Give a power series representation for the function f(x) x^3/(1 + 9x^2)

Mathematics
1 answer:
Nata [24]3 years ago
6 0

Recall that for |x|, we have

\displaystyle\frac1{1-x}=\sum_{n\ge0}x^n

Replace x with -9x^2 and we get

\displaystyle\frac1{1-(-9x^2)}=\sum_{n\ge0}(-9x^2)^n=\sum_{n\ge0}(-9)^nx^{2n}

Lastly, multiply this by x^3, so that

\boxed{f(x)=\displaystyle\sum_{n\ge0}(-9)^nx^{2n+3}}

You might be interested in
Mr. Roy is scheduled to work less than 18 hours this week. He all ready work 7 hours.If x is the remaining number of hours Mr. R
ANTONII [103]

Answer:

B and E    

Step-by-step explanation:

6 0
2 years ago
If 3 to the power y = x then y = ?
Oksanka [162]

Answer:

y=\log_3(x)


Step-by-step explanation:

3^y=x

\ln(3^y)=\ln(x)

y\ln(3)=\ln(x)

y=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

but if

f(x)=\frac{\displaystyle\ln(x)}{\displaystyle\ln(3)}

then since

f(3)=\frac{\displaystyle\ln(3)}{\displaystyle\ln(3)}=1

f(x)=\log_3(x)

so

y=\log_3(x)


or


3^y=x

\log_3(3^y)=\log_3(x)

y\log_3(3)=\log_3(x)

\text{but }\,\log_3(3)=1, \text{so,}

y=\log_3(x)



6 0
3 years ago
An apartment building produces $4,000 per quarter in gross rents. The maintenance expenses run $350 per month. Property taxes ar
erica [24]

Answer:

0.16%

Step-by-step explanation:

Cost of rent per quarter = $4000

Cost of rent per year = 4×$4000

= $16,000

This means that the apartment building produces $12,000 per year in gross rents.

Yearly Expenses are as follows;

Maintenance expenses per year = 12×$350 = $4200

Property taxes per year = $1,750

Mortgage payment per year = 12×$650 = $7800

Total expenses per year = sum of all the yearly expenses

= $4200+$1,750+$7800

= $13750

Yearly revenue generated = Cost of rent per year - total yearly expenses

= $16,000-$13750

= $2250 (net operating income)

Capitalization rate is given as the ratio of the net operating income to the market value of the building.

Capitalization rate = net operating income/market value of building

Since the building with $83750, that will be its market value

Cap rate = $13750/$83750

Cap rate = 0.16%

6 0
3 years ago
Find the value of x in 5rasised to power x=125
mestny [16]
5^3=125
Hope this helps

7 0
3 years ago
Read 2 more answers
the ordered pairs(1,4), (3,12), and (5, 20)represent the distance y that Jario walks after x seconds. Plot the ordered pairs on
murzikaleks [220]

Check the picture below.

7 0
3 years ago
Read 2 more answers
Other questions:
  • How do u write 37.025 in word form
    15·2 answers
  • A student is given the rectangle and the square shown. The student states that the two figures have the
    7·1 answer
  • Is 5 a rationl or a irratinal
    14·2 answers
  • What is a solution to the following system of equations?<br><br> x2 + y2 = 13 <br> 2x - y = 4
    15·1 answer
  • MZYX=pi/3 radians. Covert this radian measure to its equivalent degree measure.
    7·1 answer
  • The figures to the right are similar. Compare the first figure to the second. Give the ratio of the perimeters and the ratio of
    6·1 answer
  • A store charges 17 1 2 % GCT on all sales. What is the total cost of a 3 shirts if 1 is marked at J$1200?
    10·1 answer
  • What is 8% of 24?<br><br><br><br> im just putting this here bc it too short
    13·1 answer
  • Round 8.85 to the nearest hundredths.
    5·2 answers
  • 2.) Simplify:<br> 10x + 6y +4x =<br> x(14) + 6y = 14x +6y
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!