I must be an idiot...

[Dudan]

So, I was asked in class last friday...

Find S(n) and s(n) for f(x)=16 - x^2 over the interval [1,4] using n=6

I don't remember ever going over anything like this.

Any help on how to get started or what this is I'd appreciate it.

 

[pka]

So, I was asked in class last friday...
Find S(n) and s(n) for f(x)=16 - x^2 over the interval [1,4] using n=6

Without additional definitions any help would be a sheer guess.
Are you doing Riemann integrals? If so those may have to do with upper and lower sums.
But that is a guess.

 

[Dudan]

Edit: Correction, we learned Riemann sum about two weeks ago. However, my notes don't cover anything like this.

 

[pka]

Whether S(n) and s(n) represent the right and left Riemann sums respectively or vice versa is a complete mystery to me. \(\displaystyle \displaystyle \sum_{i=1}^n\left(f(x_i) * \Delta x\right).\)

As long as we are still guessing, I would think that \(\displaystyle S(n) \) is for upper sum and \(\displaystyle s(n) \) is for lower sum. In this case the function decreasing so the left-hand sum is the upper sum and right-hand sum is the lower sum.