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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/x

^{2}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 x

^{2}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/x

^{2}dx from 0 to 1

b) the integral of 1/x

^{2}dx from 0 to 1

c) the integral of 1/x

^{2}dx from 0 to 8

d) the integral of x

^{2}/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.