How do you find the area #y = f(x) = 4/x^2# , from 1 to 2 using ten approximating rectangles of equal widths and right endpoints?
See the explanation.
The bases of the rectangles are the subintervals:
The right endpoints are :
Use these to find the height of the rectangles:
Now do the arithmetic.
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To find the area under the curve ( y = f(x) = \frac{4}{x^2} ) from ( x = 1 ) to ( x = 2 ) using ten approximating rectangles of equal widths and right endpoints, follow these steps:

Determine the width of each rectangle: ( \Delta x = \frac{2  1}{10} = 0.1 ).

Calculate the right endpoints for each rectangle: ( x_i = 1 + i \cdot \Delta x ), for ( i = 1, 2, ..., 10 ).

Evaluate the function ( f(x) ) at each right endpoint: ( y_i = f(x_i) = \frac{4}{(1 + i \cdot 0.1)^2} ), for ( i = 1, 2, ..., 10 ).

Calculate the area of each rectangle: ( A_i = \Delta x \cdot y_i ), for ( i = 1, 2, ..., 10 ).

Sum up the areas of all rectangles: ( A_{\text{total}} = A_1 + A_2 + ... + A_{10} ).

Compute the total area under the curve as the approximation: ( A_{\text{total}} = \sum_{i=1}^{10} \Delta x \cdot \frac{4}{(1 + i \cdot 0.1)^2} ).
Calculate the numerical value of ( A_{\text{total}} ) to find the area under the curve from ( x = 1 ) to ( x = 2 ) using ten rectangles with 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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