anonymous
  • anonymous
Reimann Sum Continues.
Mathematics
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this
and thousands of other questions

amistre64
  • amistre64
ahhh, much better lol
anonymous
  • anonymous
lol
anonymous
  • anonymous
so i wrote down sum (-2+3i/n)(3/n)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

amistre64
  • amistre64
good, im reviewing some notes to bring me up to speed
anonymous
  • anonymous
k can you also explain to me the point of what we are doing
amistre64
  • amistre64
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
amistre64
  • amistre64
-3 lim(sum) x (3/n) is the easiest one to do, so lets start with that one :)
amistre64
  • amistre64
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
anonymous
  • anonymous
(-2+3i/n)(3/n)
amistre64
  • amistre64
(sum) (-6/n^2 + 9i/n^2)
anonymous
  • anonymous
so -6/n+9i/n
anonymous
  • anonymous
9i/n^2
amistre64
  • amistre64
your right... I got lost there for a sec :)
amistre64
  • amistre64
it says to split this one up into: (sum) -6/n+ (sum)9i/n^2
anonymous
  • anonymous
why?
anonymous
  • anonymous
adding rule?
amistre64
  • amistre64
yeah, I am suuming the adding rule :) it gets us to the (sum) i formula
anonymous
  • anonymous
k i split is up as you said
amistre64
  • amistre64
(9/n^2) (sum)i is... 9 n(n+1) ---- ------ n^2 2
anonymous
  • anonymous
ok
anonymous
  • anonymous
do we substitute that?
amistre64
  • amistre64
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 :)
anonymous
  • anonymous
k haha
anonymous
  • anonymous
so we are at (-6+(9(n+1))/2
amistre64
  • amistre64
9(n+1) ------ - 6 2n^2 -6n^2 9n 9 ----- + ---- + --- n^2 n^2 n^2
anonymous
  • anonymous
oh you just lost me
anonymous
  • anonymous
you just distributed?
amistre64
  • amistre64
lost myself too, let me redo that last part :)
amistre64
  • amistre64
9n+9 ------ - 6 2n -12n 9n 9 ----- + ---- + --- 2n 2n 2n might be better
amistre64
  • amistre64
-3 9 --- + --- = -3 as n-> inf 2 2n
anonymous
  • anonymous
yup
anonymous
  • anonymous
hold up what?
anonymous
  • anonymous
lim as n goes to infinity sum =-3?
amistre64
  • amistre64
-3/2 ..... might be a better answer for the right side of our original equation....
amistre64
  • amistre64
I forgot the denominator of 2 :)
anonymous
  • anonymous
oh because 9/2n goes to 0?
amistre64
  • amistre64
yep, when a fraction gets bigg on the bottom what happens? 1 --------------------- becomes infinitly small 100000000000000000 it approaches zero
amistre64
  • amistre64
.0000000000.....00000000000000001
anonymous
  • anonymous
yea i know, sorry stupid question
amistre64
  • amistre64
now if our f(a + i/x\) stuff was correct, then this is our right side part
anonymous
  • anonymous
we are halfway done. Should we take the cube now
amistre64
  • amistre64
ummm...... we need to drag that -3 back over and multiply it I think :) -9/2
anonymous
  • anonymous
cool 9/2
anonymous
  • anonymous
not negative
amistre64
  • amistre64
-3(-3/2) = 9/2 that s right.... tell me im wrong :) i dont mind
amistre64
  • amistre64
since its just: (sum) x^3 we can take our f^(x_1) and work it thru
anonymous
  • anonymous
so (-2+3i/n)^3?
amistre64
  • amistre64
yep, and I am assuming that that is correct :) otherwise we are getting good practice, but the wrong results :)
anonymous
  • anonymous
at least we have the answer so we will know
anonymous
  • anonymous
its 3/4 if you forgot
amistre64
  • amistre64
whaaa!!????
anonymous
  • anonymous
the entire answer is 3/4
amistre64
  • amistre64
yeah yeah...maybe..well see :)
anonymous
  • anonymous
want me to distribute the cube?
amistre64
  • amistre64
yep, cube it out so we can multiply our 3/n to it and apply the (sum) i^3 formula to it
anonymous
  • anonymous
k give me a second
amistre64
  • amistre64
gonna swig some coffee..... bad mormon....BAD!!
anonymous
  • anonymous
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)
anonymous
  • anonymous
simplified loll (-8+36i/n-54i^2/n^2+27i^3/n^3)(3/n)
anonymous
  • anonymous
distributing the 3/n : (-24/n+108i/n^2-162i^2/n^3+81i^3/n^4)
anonymous
  • anonymous
made me do all the dirty work ahhaah
amistre64
  • amistre64
thats what I get too :)
anonymous
  • anonymous
sweet
amistre64
  • amistre64
now lets divvy put the "i" factors
anonymous
  • anonymous
now we take each summation?
amistre64
  • amistre64
yupp
anonymous
  • anonymous
what does -24/n become
anonymous
  • anonymous
do i just pull it out?
amistre64
  • amistre64
sum_-24/n +108/n^2 sum_i -162/n^3sum_i^2 +81/n^4 sum_i^3
anonymous
  • anonymous
thats what i got
amistre64
  • amistre64
muplitiply each one by the appropriate sum i^x formulas :)
anonymous
  • anonymous
i have to go soon, are we almost done?
amistre64
  • amistre64
not even close :) I can do it quicker on the paper probably.... how long you got?
anonymous
  • anonymous
5 minutes
anonymous
  • anonymous
can you attach the image after?
amistre64
  • amistre64
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 :)
anonymous
  • anonymous
sounds good, that would be great. Sorry that i have to go.
amistre64
  • amistre64
'sok, have fun....:)
anonymous
  • anonymous
for that first one i got (108n^2+108)/2n^2
anonymous
  • anonymous
ill come back later to see if you posted and if you are still online, i may ask you questions
anonymous
  • anonymous
take care, you are a Hero for sure! haha
anonymous
  • anonymous
Hey Im back, are you there? Its kinda late but did you finish?
amistre64
  • amistre64
Here it is
1 Attachment
anonymous
  • anonymous
Wow amazing! You broke everything down
anonymous
  • anonymous
You really helped me. I can't thank you enough

Looking for something else?

Not the answer you are looking for? Search for more explanations.