ƒ(x)
Nov15-09, 08:48 AM
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.
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.