Find L_{3}(f) and U_{3}(f) for the function f(x) =1/(x+1)and the interval [a,b] = [0,3].
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Originally Posted by chizmin10 Find L_{3}(f) and U_{3}(f) for the function f(x) =1/(x+1)and the interval [a,b] = [0,3]. Please define $\displaystyle L_3(f)~\&~U_3(f)$. Please give an exact definition.
The U is the n-th upper sum for f and the L is the n-th lower sum for f.
Originally Posted by chizmin10 The U is the n-th upper sum for f and the L is the n-th lower sum for f. Draw a graph. You will see that the function is decreasing on $\displaystyle [0,3]$. That means that an upper sum is a left-hand sum and a lower sum is a right-hand sum. Because $\displaystyle n=3$ we have $\displaystyle \Delta x=1$.
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