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13 Nov 2019
EXERCISES These exercises are intended to help you practice and become fluent with the BASIC learning objectives. They can be done either during or after your reading and video watching. Work these out on paper for your records, and then you will be asked to submit the results on a web form at the end. Evaluate the sum Σ 0(H-2i-1) Suppose we are estimating the area under the graph of the function f (x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a Riemann sum with 8 subintervals of equal width, what is the value of ÎÏ? 1. 2. 3. Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a left Riemann sum with 8 subintervals of equal width, what are the left endpoints that we will use? (Note: There should be 8 of them.) Suppose we are estimating the area under the graph of the function f (x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a right Riemann sum with 8 subintervals of equal width, what are the right endpoints that we will use? Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a midpoint Riemann sum with 8 subintervals of equal width, what are the midpoints that we will use? 4. 5. 6. Now suppose f(x)-10-10 Use a midpoint Riemann sum with n = 4 rectangles to estimate the area under the graph of this function and above the x-axis. 7. Repeat the previous question, using a left Riemann sum with n6 rectangles. 8. Draw pictures of the rectangles used for exercises 6 and 7, like you see in the Preview Activity for this section. Based on the visuals, which appears to be a better approximation to the true area under the curve: A midpoint sum with 4 rectangles, or a left-hand sum with 6 rectangles? Explain.
EXERCISES These exercises are intended to help you practice and become fluent with the BASIC learning objectives. They can be done either during or after your reading and video watching. Work these out on paper for your records, and then you will be asked to submit the results on a web form at the end. Evaluate the sum Σ 0(H-2i-1) Suppose we are estimating the area under the graph of the function f (x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a Riemann sum with 8 subintervals of equal width, what is the value of ÎÏ? 1. 2. 3. Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a left Riemann sum with 8 subintervals of equal width, what are the left endpoints that we will use? (Note: There should be 8 of them.) Suppose we are estimating the area under the graph of the function f (x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a right Riemann sum with 8 subintervals of equal width, what are the right endpoints that we will use? Suppose we are estimating the area under the graph of the function f(x) (which is always positive) and above the x-axis, on the interval [2, 6]. If we use a midpoint Riemann sum with 8 subintervals of equal width, what are the midpoints that we will use? 4. 5. 6. Now suppose f(x)-10-10 Use a midpoint Riemann sum with n = 4 rectangles to estimate the area under the graph of this function and above the x-axis. 7. Repeat the previous question, using a left Riemann sum with n6 rectangles. 8. Draw pictures of the rectangles used for exercises 6 and 7, like you see in the Preview Activity for this section. Based on the visuals, which appears to be a better approximation to the true area under the curve: A midpoint sum with 4 rectangles, or a left-hand sum with 6 rectangles? Explain.
Bunny GreenfelderLv2
16 Jun 2019