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2 years ago

Please I need help fast please help me

Mathematics

1 answer:

Effectus [21]2 years ago

5 0

Answer: 0-o uhhhh 0-o

uhhhh0-o

Step-by-step explanation:

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Now, lets evaluate the same integral using power series. first, find the power series for the function f(x = \frac{32}{x^2+4}. t

BlackZzzverrR [31]

No idea what the previous part of the problem is, but you have

$f(x)=\dfrac{32}{x^2+4}=\dfrac8{1-\left(-\frac{x^2}4\right)}=\displaystyle8\sum_{n\ge0}\left(-\frac{x^2}4\right)^n$
$f(x)=\displaystyle8\sum_{n\ge0}\left(-\dfrac14\right)^nx^{2n}$

which is valid for $\left|-\dfrac{x^2}4\right|$ , or $|x|$ . So the integral from 0 to 2 is

$\displaystyle\int_0^2f(x)\,\mathrm dx=\int_0^28\sum_{n\ge0}\left(-\frac14\right)^nx^{2n}\,\mathrm dx$
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\int_0^2x^{2n}\,\mathrm dx$

Note that since the power series only converges on the interval if $x$ is strictly less than 2, which means we have to treat this as an improper integral.

$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\int_0^tx^{2n}\,\mathrm dx$ [/tex]
$=\displaystyle8\sum_{n\ge0}\left(-\frac14\right)^n\lim_{t\to2^-}\frac{x^{2n+1}}{2n+1}\bigg|_{x=0}^{x=t}$
$=\displaystyle8\sum_{n\ge0}\frac{(-1)^n}{2^{2n}(2n+1)}\lim_{t\to2^-}t^{2n+1}$
$=\displaystyle16\sum_{n\ge0}\frac{(-1)^n}{2n+1}$
$=16-\dfrac{16}3+\dfrac{16}5-\dfrac{16}7+\dfrac{16}9+\cdots$

6 0

2 years ago

The second term of an arithmetic sequence is -39. The rule a, = a -1 + 12 can be used to find the next term of the

siniylev [52]

Step-by-step explanation:

the first one is the correct one

a, = -51+12(n-1)

a(2) = -51+12(2-1)=-39

I hope this helps

Im sure from the answer

but I couldnt explain it exactly

4 0

2 years ago

Read 2 more answers

Please help with question 6

Kitty [74]

Answer:

y = -3x - 1

Use the methods on your other questions.

6 0

2 years ago

2. It costs Edgar $2.65 one way to ride the bus to work. He uses the bus to go to and from work four days per week. He buys a bo

Maurinko [17]

$27

2.65 x 2 (since he has to go both to and from work each day) = $5.30
Add the daily cost of the water bottle (1.45) to make his total cost for one day, which is 6.75
Multiply this number by 4 (because he goes 4 days a week) to get $27 for one week.

6 0

2 years ago

Math 9. please help, and show work :)

galina1969 [7]

3.5 cm from the centre

8 0

2 years ago