Question

Hey guys, I am looking for some help with calculus. It is in regard to rieman sums, and I would really appreciate any help understanding. I will post links below and explain further.

Answer 1

The graph shown is y=x

I just dont see how those steps were derived

Answer 2

And this is part of it also

Answer 3

Is therom 5 something that must be memorized? Or is there any logic to it?

Answer 4

What does k represent?

Answer 5

k is from 1 to n, if you notice the summation sign in your first photo

Answer 6

But why is that over n the height?

Answer 7

And is the width 1/n just because we are taking it as n approaches infinity? so therefor 1/n is approach infinitely small?

Answer 8

@kc_kennylau ?

Answer 9

yes, and sorry I'm not too familiarized in this topic... furthermore i'm busy :'(

Answer 10

sorry :'(

Answer 11

Thanks for the input anyways kc!

Answer 12

Ok I can try drawing a picture for you and posting it. But first let's see if you can see the pattern first.
so the very first number is a_1=(1-1)/n
the next number is a_2=(2-1)/n=1/n <---this is how for we are away from 0 or a_1 since a_1 is 0
a_3=(3-1)/n
....
now going to the kth interval where we have the x-value being a_k=(k-1)/n
...
going all the way to the nth interval we have a_n=(n-1)/n because we are plugging in the left end point of that interval and not the right endpoint because we are doing left-endpoint rule
we are taking all the left endpoints of all the n intervals beginning at 0

Answer 13

Now to find the heights of the rectangles we do f(a_k)

Answer 14

By a_1 does that mean a/1?