Help me as soon as possible thanks

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

3 years ago

What is the value of -2/5 divided by 6/8 PLEASE HELPPP

Tatiana [17]

Answer:

The steps to do :

$- \frac{2}{5} \div \frac{6}{8}$

$= - \frac{2}{5} \times \frac{8}{6}$

$= - \frac{1}{5} \times \frac{8}{3}$

$= - \frac{1 \times 8}{5 \times 3}$

$= - \frac{8}{15}$

7 0

3 years ago

Barrett is comparing the membership fees for two museums.The art museum charges a one-time fee of $8.25 plus $2.25 per month. Th

Oksanka [162]

Answer:

$2.50+$1.25 times M

Step-by-step explanation:

$10.75-$8.25=$2.50

$3.50-$2.25=$1.25

$2.50+$1.25=$3.75

As only one-time fee, we cancel out it, then only add on the per-month fee, which is $1.25 every month.

7 0

3 years ago

How to solve this equation 7-2a-5-14=-2+3a

SSSSS [86.1K]

To solve 7-2a-5-14=-2+3a :

1) combine like terms: 7-19 - 2a = -2 + 3a, and then -10 = 5a

2) solve this equation for a: a = -10/5 = -2.

The solution of 7-2a-5-14=-2+3a is a = -2.

6 0

3 years ago

Read 2 more answers

what is fourteen less than five times a number is three times the number and what is twelve more than seven times a number equal

andrey2020 [161]

If I am reading the equations correctly, they are:
5x - 14 = 3x AND 7x + 12 = x - 6

If this is correct, the first one would be worked out like this:
5x (- 5x) - 14 = 3x (- 5x)
- 14 = - 2x
- 14 (/ - 2) = - 2x (/ - 2)
7 = x

The second would be worked out like this:
7x + 12 (+ 6) = x - 6 (+ 6)
7x + 18 = x
7x (- 7x) + 18 = x (- 7x)
18 = - 6x
18 (/ - 6) = - 6x (/ - 6)
- 3 = x

I hope this is what you are looking for :)

8 0

3 years ago