Riemann sums

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These questions are ones that my teacher never explained:

1) if c is a positive integer, then the limit of (1/c)(1/c + 2/c ... + 5c/c) as c approaches infinity can be expressed as

a) integral of x^2 dx from 0 to 1
b) integral of 1/x dx from 0 to 5
c) integral of x dx from -5 to 5
d) integral of x dx from 0 to infinity
e) integral of x dx from 0 to 5

2) the limit as n approaches infinity of (1/n)( (n/1)2 + (n/2)2 + ... + (n/n)2) =

a) the integral of 1/x2 dx from 0 to 1
b) the integral of 1/x dx from 0 to 1
c) the integral of x dx from 0 to 1
d) the integral of x2 dx from 0 to 1
e) none of the above

3) if u is a positive integer, then the limit of (1/u)( (2/u)2 + (4/u)2 + .... + (8u/u)2) can be expressed as

a) the integral of 8/x2 dx from 0 to 1
b) the integral of 1/x2 dx from 0 to 1
c) the integral of 1/x2 dx from 0 to 8
d) the integral of x2/2 dx from 0 to 8

I later found out that the answers were e,a, and d in that order but still need an explaination.
 

Answers and Replies

  • #2
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Ok. Now I realize where the start and end points for the integral come from. But not the rest.
 
  • #3
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Anyone?

Also, I think its the limit of the sum of .... whatever expression is there.
 
Last edited:

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