William W. answered • 12/20/21
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This function is decreasing on the interval [-3, 1] so the upper limit is the left hand Riemann Sum. The calculation will be a terrible estimate with only 2 rectangles:
I can't even show the second rectangle because it's so small in this scale.
The area is the height of the rectangle times it's width = f(-3) • 2 + f(-1) • 2
William W.
The “upper sum” is an estimate of the area under the curve. In order to estimate it, we can use a series of rectangles and use simple methods (length times width) to find the areas of those rectangles and add them up. Usually, the more rectangles used, the closer the estimate is to the real area. But, of course, for a finite number of rectangles, the tops of those rectangles don’t match the curve well because the rectangle is square on top and the “curve” (function graph line) is not. So, there will be an overestimate if one corner of the rectangle touches the curve and an underestimate if the other corner of the rectangle touches the curve. Does any of this sound familiar to what you are learning in your lectures?
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12/21/21
Natasha W.
Find the upper sum for f(x)=1−x/5 on the interval [−3,1] using 2 rectangles. im not sure if that helps answer the question a bit ?12/20/21