How do you estimate the area under the graph of #f(x)= 2/x# on [1,5] into 4 equal subintervals and using right endpoints?
Use
In this question the subintervals are:
The heights at the endpoints are:
So the area is approximately:
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To estimate the area under the graph of ( f(x) = \frac{2}{x} ) on the interval ([1, 5]) using four equal subintervals and right endpoints, you can follow these steps:

Divide the interval ([1, 5]) into four equal subintervals: ([1, 2]), ([2, 3]), ([3, 4]), and ([4, 5]).

Calculate the width of each subinterval: ( \Delta x = \frac{b  a}{n} = \frac{5  1}{4} = \frac{4}{4} = 1 ).

Determine the right endpoints of each subinterval: For the four subintervals, the right endpoints are ( x = 2 ), ( x = 3 ), ( x = 4 ), and ( x = 5 ).

Evaluate the function ( f(x) = \frac{2}{x} ) at the right endpoints:
 At ( x = 2 ): ( f(2) = \frac{2}{2} = 1 )
 At ( x = 3 ): ( f(3) = \frac{2}{3} )
 At ( x = 4 ): ( f(4) = \frac{2}{4} = \frac{1}{2} )
 At ( x = 5 ): ( f(5) = \frac{2}{5} )

Calculate the area of each rectangle formed by the function values and the width of the subinterval:
 For the subinterval ([1, 2]), the area is ( 1 \times 1 = 1 )
 For the subinterval ([2, 3]), the area is ( \frac{2}{3} \times 1 )
 For the subinterval ([3, 4]), the area is ( \frac{1}{2} \times 1 = \frac{1}{2} )
 For the subinterval ([4, 5]), the area is ( \frac{2}{5} \times 1 )

Sum up the areas of all four rectangles to estimate the total area under the graph of ( f(x) ) on the interval ([1, 5]) using right endpoints.
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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.
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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