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4 years ago

69x^2y^3,84xy^2,108x^3y^3

Mathematics

1 answer:

pishuonlain [190]4 years ago

5 0

So what do you want? to multiply it?

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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

3 years ago

Please Help 6-10 or just one of them

Free_Kalibri [48]

Answer:

6) 20

7) I think is 2.5 (im not sure)

8) 7

Step-by-step explanation:

6) (5x+9)+(3x+11)=180

8x+20=180

-20 -20

8x=160

Divide 8 on each side

x=20

7) (17x+1)=(20x-14)

17x+15 =20x

+17 +17

15 = 37x

divide 15 on each side

X=2.5

8) (3x+3)+(10-4)=90

(3x)+(10x-1)

13x-`1=90

+1 +1

13x=91

Divide 13 on each side

x=7

5 0

3 years ago

Eigthy millimetes as a percentage of one metre is<br>8<br>80<br>800<br>8000

Anit [1.1K]

Answer:

8%.

Step-by-step explanation:

There are 1000 millimeters in 1 meter.

So the percentage is (80/1000) * 100

= 80/10

= 8%.

7 0

3 years ago

Read 2 more answers

How do you get the crown things

Anvisha [2.4K]

You have to start answer more questions daily in which ever field you are best in

8 0

3 years ago

What is the slope of the line that passes through the points (5,8) and ( 11, 8)?

LenaWriter [7]

(5, 8) and (11, 8)

(y - yo) = m.(x - xo)

(8 - 8) = m.(11 - 5)

0 = m.6

m = 0

So,

(y - yo) = 0.(x - xo)

(y - yo) = 0

y = yo

y = 8

7 0

3 years ago