anonymous
  • anonymous
:( this question is killing me Write the limit as n goes to infinity of the summation from k equals 1 of the product of the 3rd power of the quantity 2 plus 5 times k over n and 5 over n as a definite integral.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
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anonymous
  • anonymous
@amistre64 @welshfella any ideas?
anonymous
  • anonymous
not really sure how to go about this one.

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anonymous
  • anonymous
@Preetha @nincompoop @Hero @Luigi0210 @Nnesha
amistre64
  • amistre64
what is the limit of 5/n as n to infinity?
amistre64
  • amistre64
the limit of a product is the product of the limits, if i recall correctly .. but you want the summation limit
anonymous
  • anonymous
0?
amistre64
  • amistre64
yes, now if there is some useful way to rewrite the argument ...
amistre64
  • amistre64
(a+b)^3 = 1a^3b^0 +3a^2b^1 +3a^1b^2 +1a^0b^3
anonymous
  • anonymous
im sorry i dont follow
amistre64
  • amistre64
im wondering if we expand the ^3 part, if we cant see this thing easier, or make it funner to play with.
anonymous
  • anonymous
i dont think that would make a difference
amistre64
  • amistre64
40/n + 300k/(n^2) +750k^2/(n^3) + 625k^3/(n^4) youre prolly right
amistre64
  • amistre64
well, by simply putting in a large number for n http://www.wolframalpha.com/input/?i=sum%28n%3D1+to+100000%29+of+5%282%2Bn%285%2F100000%29%29^3%2F100000
anonymous
  • anonymous
don't really need to find the limit though just need to know how to write it as an integral
anonymous
  • anonymous
do you know anyone that could solve this , im sort of new to openstudy don't know anyone :(
amistre64
  • amistre64
oh, i gave up trying to read the whole question when the numbers were written out in words ...
amistre64
  • amistre64
so this is a reimann sum thing
anonymous
  • anonymous
yes can you open this picture ?
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amistre64
  • amistre64
\[\Large\sum_{k=a}^{b}f(a+i\frac{b-a}{n})\frac{b-a}{n}\color{red}\implies \int_{a}^{b}f(x)dx\]
amistre64
  • amistre64
ach ... im used to i instead of k so theres some bleed over there
amistre64
  • amistre64
the picture is fine ...
amistre64
  • amistre64
k=0 to n, not a to b
amistre64
  • amistre64
does that seem familiar?
anonymous
  • anonymous
yes sort of let me try to write it out
amistre64
  • amistre64
1 to n is a right hand rule, 0 to n-1 is a left had rule ... im working from memory is all
amistre64
  • amistre64
either way... a=2, and b-a = 5 soo b=7 seems right
amistre64
  • amistre64
i would venture to say f(x) = x^3, but my brain is telling me to be ware of that assumption
anonymous
  • anonymous
how would you find k?
amistre64
  • amistre64
k is just the kth iteration of the partition
anonymous
  • anonymous
okay so what about n?
amistre64
  • amistre64
|dw:1439506802530:dw|
amistre64
  • amistre64
n is the number of partitions overall, as n to infinity the discrete reimann sum becomes a definite integral ... the area beneath the curve from a to b
anonymous
  • anonymous
i see , what makes ou think that f(x) = x^3 how would you usually go about finding f(x)?
amistre64
  • amistre64
http://www.wolframalpha.com/input/?i=integrate+x^3+dx%2C+from+2+to+7 the good news is that my assumption is good lol
amistre64
  • amistre64
well the (...)^3 is a good indicator that the function is akin to x^3
anonymous
  • anonymous
oh that value that i thought would be useless XD
anonymous
  • anonymous
okay great thank you for your help
anonymous
  • anonymous
how do i do the b=medal thingy?
amistre64
  • amistre64
youre welcome :) thnx for the recollections lol
amistre64
  • amistre64
there should be a "best response" button in everything i post ... just click it to give a medal to someone
anonymous
  • anonymous
thank you again ! :D
amistre64
  • amistre64
yep, and good luck ;)

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