:( 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.

- anonymous

- katieb

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- anonymous

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- anonymous

@amistre64 @welshfella any ideas?

- anonymous

not really sure how to go about this one.

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## More answers

- anonymous

- amistre64

what is the limit of 5/n as n to infinity?

- amistre64

the limit of a product is the product of the limits, if i recall correctly .. but you want the summation limit

- anonymous

0?

- amistre64

yes, now if there is some useful way to rewrite the argument ...

- amistre64

(a+b)^3 = 1a^3b^0 +3a^2b^1 +3a^1b^2 +1a^0b^3

- anonymous

im sorry i dont follow

- amistre64

im wondering if we expand the ^3 part, if we cant see this thing easier, or make it funner to play with.

- anonymous

i dont think that would make a difference

- amistre64

40/n + 300k/(n^2) +750k^2/(n^3) + 625k^3/(n^4)
youre prolly right

- 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

don't really need to find the limit though just need to know how to write it as an integral

- anonymous

do you know anyone that could solve this , im sort of new to openstudy don't know anyone
:(

- amistre64

oh, i gave up trying to read the whole question when the numbers were written out in words ...

- amistre64

so this is a reimann sum thing

- anonymous

yes can you open this picture ?

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- 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

ach ... im used to i instead of k so theres some bleed over there

- amistre64

the picture is fine ...

- amistre64

k=0 to n, not a to b

- amistre64

does that seem familiar?

- anonymous

yes sort of let me try to write it out

- 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

either way... a=2, and b-a = 5 soo b=7 seems right

- amistre64

i would venture to say f(x) = x^3, but my brain is telling me to be ware of that assumption

- anonymous

how would you find k?

- amistre64

k is just the kth iteration of the partition

- anonymous

okay so what about n?

- amistre64

|dw:1439506802530:dw|

- 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

i see , what makes ou think that f(x) = x^3
how would you usually go about finding f(x)?

- 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

well the (...)^3 is a good indicator that the function is akin to x^3

- anonymous

oh that value that i thought would be useless XD

- anonymous

okay great thank you for your help

- anonymous

how do i do the b=medal thingy?

- amistre64

youre welcome :) thnx for the recollections lol

- amistre64

there should be a "best response" button in everything i post ... just click it to give a medal to someone

- anonymous

thank you again ! :D

- amistre64

yep, and good luck ;)

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