Question

I need help with Reimann sum for evaluating a limit.

Answer 1

where you stuck at?

Answer 2

I need help starting off

Answer 3

might help to write out the first few iterations, n=1,2,3 ... but thats just a thought

Answer 4

ok one sec

Answer 5

4/1 (sqrt(4(1)/(1))

4/2 (sqrt(4(1)/(2)+sqrt(4(2)/(2))

4/3 (sqrt(4(1)/(3)+sqrt(4(2)/(3)+sqrt(4(3)/(3))

4/4 (sqrt(4(1)/(4)+sqrt(4(2)/(4)+sqrt(4(3)/(4)+sqrt(4(4)/(4))

\[\sum_{k=1}^{n}\frac{4}{n}\sqrt{\frac{4k}{n}}\]

looks like a right side type of problem to me

Answer 6

right side?

Answer 7

yeah, the value of the function on the right side of a 'rectangle'

Answer 8

oh ok yea I think I know what u mean

Answer 9

\[\sum_{i=1}^{n} f(a+i\frac{b-a}{n})\frac{b-a}{n}\]

Answer 10

4-0 = 4

a = 0

wouldnt this be the integral of sqrt(x), from 0 to 4?

Answer 11

yea

Answer 12

So then I just use the fundamental theorem on this correct?

Answer 13

might as well :)

Answer 14

I got 16/3

Answer 15

we can assess a similar function, -x^2 +4, from 0 to 2

-x^3/3 +4x, at x=2

8-8/3 = (24-8)/3 .. yeah 16/3

Answer 16

ok awesome Thanks for the help

Answer 17

yep :)