How do you use n = 5 equally divided subdivisions to estimate the integral from 1 to 3 of #(1/x^2)dx# with the righthand Riemann sum?
See the explanation.
The subintervals are:
The right endpoints are:
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To estimate the integral from 1 to 3 of ( \frac{1}{x^2} ) using the righthand Riemann sum with ( n = 5 ) equally divided subdivisions, follow these steps:

Calculate the width of each subdivision, ( \Delta x ), by dividing the total interval length by the number of subdivisions: [ \Delta x = \frac{3  1}{5} = \frac{2}{5} ]

Determine the endpoints of each subdivision. Since we are using righthand Riemann sum, the right endpoint of each subdivision will be used for evaluation.

Evaluate the function ( \frac{1}{x^2} ) at the right endpoint of each subdivision.

Multiply each function value by the width of the subdivision, ( \Delta x ).

Sum up all these products. This sum represents the estimate of the integral using the righthand Riemann sum with ( n = 5 ) subdivisions.

The formula for the righthand Riemann sum is: [ R_n = \sum_{i=1}^{n} f(x_i^) \Delta x ] where ( x_i^ ) is the right endpoint of the ( i )th subdivision.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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