How do you calculate the left and right Riemann sum for the given function over the interval [0, ln2], using n=40 for #e^x#?
Left Riemann sum
Right Riemann sum
and the sum is given by:
The left Riemann sum is:
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To calculate the left and right Riemann sums for the given function ( f(x) = e^x ) over the interval ([0, \ln 2]) using ( n = 40 ), follow these steps:

Partition the Interval: Divide the interval ([0, \ln 2]) into ( n ) subintervals of equal width. Since ( n = 40 ), each subinterval will have a width of ( \frac{\ln 2}{40} ).

Calculate Sample Points: For the left Riemann sum, choose the left endpoint of each subinterval as the sample point. For the right Riemann sum, choose the right endpoint of each subinterval.

Evaluate Function Values: Evaluate the function ( f(x) = e^x ) at each of the chosen sample points.

Sum Up the Areas: Multiply each function value by the width of the corresponding subinterval and sum up these products.

Finalize: The sum obtained in step 4 for the left Riemann sum represents the approximation of the area under the curve using left endpoints, and for the right Riemann sum, it represents the approximation using right endpoints.
By following these steps, you can calculate the left and right Riemann sums for the given function over the specified interval using ( n = 40 ).
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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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