Question

Reimann Sum Continues.

Answer 1

ahhh, much better lol

Answer 2

lol

Answer 3

so i wrote down sum (-2+3i/n)(3/n)

Answer 4

good, im reviewing some notes to bring me up to speed

Answer 5

k can you also explain to me the point of what we are doing

Answer 6

the original equation:

x^3 -3x can be split into easier parts

x^3 and -3x

we use the reimann sum formulas for (sum)x^3 and (sum)x to work these to completion

Answer 7

-3 lim(sum) x (3/n) is the easiest one to do, so lets start with that one :)

Answer 8

we determined that f(x_i) = (-2+3i)/n right? so if the notes are correct, and I dont see any reason to dispute them, we multiply:

(-2+3i)/n with 3/n

Answer 9

(-2+3i/n)(3/n)

Answer 10

(sum) (-6/n^2 + 9i/n^2)

Answer 11

so -6/n+9i/n

Answer 12

9i/n^2

Answer 13

your right... I got lost there for a sec :)

Answer 14

it says to split this one up into:

(sum) -6/n+ (sum)9i/n^2

Answer 15

why?

Answer 16

adding rule?

Answer 17

yeah, I am suuming the adding rule :) it gets us to the (sum) i formula

Answer 18

k i split is up as you said

Answer 19

(9/n^2) (sum)i is...

9 n(n+1)
---- ------
n^2 2

Answer 20

ok

Answer 21

do we substitute that?

Answer 22

9n(n+1) 9(n+1)
------- = ------
2n^2 2n

now work the other part:

-6/n -> 1/n (sum) -6 = (1/n)(-6n) = -6 why? dunno, its just the example I got to go by :)

Answer 23

k haha

Answer 24

so we are at (-6+(9(n+1))/2

Answer 25

9(n+1)
------ - 6
2n^2

-6n^2 9n 9
----- + ---- + ---
n^2 n^2 n^2

Answer 26

oh you just lost me

Answer 27

you just distributed?

Answer 28

lost myself too, let me redo that last part :)

Answer 29

9n+9
------ - 6
2n

-12n 9n 9
----- + ---- + ---
2n 2n 2n

might be better

Answer 30

-3 9
--- + --- = -3 as n-> inf
2 2n

Answer 31

yup

Answer 32

hold up what?

Answer 33

lim as n goes to infinity sum =-3?

Answer 34

-3/2 ..... might be a better answer for the right side of our original equation....

Answer 35

I forgot the denominator of 2 :)

Answer 36

oh because 9/2n goes to 0?

Answer 37

yep, when a fraction gets bigg on the bottom what happens?

1
--------------------- becomes infinitly small
100000000000000000 it approaches zero

Answer 38

.0000000000.....00000000000000001

Answer 39

yea i know, sorry stupid question

Answer 40

now if our f(a + i/x\) stuff was correct, then this is our right side part

Answer 41

we are halfway done. Should we take the cube now

Answer 42

ummm...... we need to drag that -3 back over and multiply it I think :)

-9/2

Answer 43

cool 9/2

Answer 44

not negative

Answer 45

-3(-3/2) = 9/2 that s right.... tell me im wrong :) i dont mind

Answer 46

since its just: (sum) x^3 we can take our f^(x_1) and work it thru

Answer 47

so (-2+3i/n)^3?

Answer 48

yep, and I am assuming that that is correct :)

otherwise we are getting good practice, but the wrong results :)

Answer 49

at least we have the answer so we will know

Answer 50

its 3/4 if you forgot

Answer 51

whaaa!!????

Answer 52

the entire answer is 3/4

Answer 53

yeah yeah...maybe..well see :)

Answer 54

want me to distribute the cube?

Answer 55

yep, cube it out so we can multiply our 3/n to it and apply the (sum) i^3 formula to it

Answer 56

k give me a second

Answer 57

gonna swig some coffee..... bad mormon....BAD!!

Answer 58

k here it is non simplified: ( -8+12i/n+12i/n-18i^2/n^2+12i/n-18i^2/n^2-18i^2/n^2+27i^3/n^3)(3/n)

Answer 59

simplified loll (-8+36i/n-54i^2/n^2+27i^3/n^3)(3/n)

Answer 60

distributing the 3/n : (-24/n+108i/n^2-162i^2/n^3+81i^3/n^4)

Answer 61

made me do all the dirty work ahhaah

Answer 62

thats what I get too :)

Answer 63

sweet

Answer 64

now lets divvy put the "i" factors

Answer 65

now we take each summation?

Answer 66

yupp

Answer 67

what does -24/n become

Answer 68

do i just pull it out?

Answer 69

sum_-24/n
+108/n^2 sum_i

-162/n^3sum_i^2

+81/n^4 sum_i^3

Answer 70

thats what i got

Answer 71

muplitiply each one by the appropriate sum i^x formulas :)

Answer 72

i have to go soon, are we almost done?

Answer 73

not even close :) I can do it quicker on the paper probably....

how long you got?

Answer 74

5 minutes

Answer 75

can you attach the image after?

Answer 76

aint gonna happen in 5 minutes :) I can work it out and post it here if youd like, might even figure out where I go wrong and learn something :)

Answer 77

sounds good, that would be great. Sorry that i have to go.

Answer 78

'sok, have fun....:)

Answer 79

for that first one i got (108n^2+108)/2n^2

Answer 80

ill come back later to see if you posted and if you are still online, i may ask you questions

Answer 81

take care, you are a Hero for sure! haha

Answer 82

Hey Im back, are you there? Its kinda late but did you finish?

Answer 83

Here it is

Answer 84

Wow amazing! You broke everything down

Answer 85

You really helped me. I can't thank you enough