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hali
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Find the limit limn→∞∑i=1 i/n^2+i^2 by expressing it as a definite integral of an appropriate
function via Riemann sums
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function via Riemann sums
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A Riemann Sum is a method used to approximate the area under a curve by dividing the region into smaller rectangles and finding the sum of their areas.
Finding the limit of a sum using Riemann Sums allows us to accurately determine the area under a curve, which has many practical applications in fields such as physics, economics, and engineering.
A left Riemann Sum uses the left endpoint of each subinterval to determine the height of the rectangle, while a right Riemann Sum uses the right endpoint. This can result in slightly different approximations of the area under the curve.
The more subintervals used, the more accurate the approximation will be. However, using too many subintervals can be computationally intensive. It is important to find a balance between accuracy and efficiency when choosing the number of subintervals.
As the width of the subintervals gets smaller, the Riemann Sum approaches the actual area under the curve, known as the definite integral. This is why taking the limit of a Riemann Sum allows us to accurately find the area under a curve.