For the second approximation A, we subdivide the 0 to 1 interval into two equal parts....
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For the second approximation A₂, we subdivide the 0 to 1 interval into two equal parts. This gives us two rectangles, each touching the curve at its top-right corner. 2. Draw the image shown at right on your paper. Then compute A₂. Show your steps. 3. Let s skip A3 and go straight to A4. Subdivide the 0 to 1 interval into four equal parts. Draw a new image of the axes and the curve. Draw four rectangles, each touching the curve at its top-right corner. The compute A4. rds For the second approximation A₂, we subdivide the 0 to 1 interval into two equal parts. This gives us two rectangles, each touching the curve at its top-right corner. 2. Draw the image shown at right on your paper. Then compute A₂. Show your steps. 3. Let s skip A, and go straight to A4. Subdivide the 0 to 1 interval into four equal parts. Draw a new image of the axes and the curve. Draw four rectangles, each touching the curve at its top-right corner. The compute A4. 4. Because of the way we have set up our rectangles, our approximations are all over-estimates. Notice that the more rectangles we use, the better our approximations. Unfortunately, this also means more arithmetic to work out. It would be no small task to compute A100. Instead, let s approach the problem more generally. a) Draw the axes and the curve once again. This time, subdivide the 0 to 1 interval into ten equal parts, like in the graph above, but only draw the first four rectangles and the last rectangle. There are rectangles in-between, but we will leave them undrawn. b) Now as you think about this, ignore the fact that there are ten subdivisions. Maybe there are nine, or maybe eleven, or maybe there are many more. Instead of thinking about the number of rectangles as a fixed number, think of them as a varying amount. We will say there are n rectangles. Assuming these n rectangles have equal width, find an expression for this width. English (United States ZOT MacBook Air tv D For the second approximation A₂, we subdivide the 0 to 1 interval into two equal parts. This gives us two rectangles, each touching the curve at its top-right corner. 2. Draw the image shown at right on your paper. Then compute A₂. Show your steps. 3. Let s skip A3 and go straight to A4. Subdivide the 0 to 1 interval into four equal parts. Draw a new image of the axes and the curve. Draw four rectangles, each touching the curve at its top-right corner. The compute A4. rds For the second approximation A₂, we subdivide the 0 to 1 interval into two equal parts. This gives us two rectangles, each touching the curve at its top-right corner. 2. Draw the image shown at right on your paper. Then compute A₂. Show your steps. 3. Let s skip A, and go straight to A4. Subdivide the 0 to 1 interval into four equal parts. Draw a new image of the axes and the curve. Draw four rectangles, each touching the curve at its top-right corner. The compute A4. 4. Because of the way we have set up our rectangles, our approximations are all over-estimates. Notice that the more rectangles we use, the better our approximations. Unfortunately, this also means more arithmetic to work out. It would be no small task to compute A100. Instead, let s approach the problem more generally. a) Draw the axes and the curve once again. This time, subdivide the 0 to 1 interval into ten equal parts, like in the graph above, but only draw the first four rectangles and the last rectangle. There are rectangles in-between, but we will leave them undrawn. b) Now as you think about this, ignore the fact that there are ten subdivisions. Maybe there are nine, or maybe eleven, or maybe there are many more. Instead of thinking about the number of rectangles as a fixed number, think of them as a varying amount. We will say there are n rectangles. Assuming these n rectangles have equal width, find an expression for this width. English (United States ZOT MacBook Air tv D
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Related Book For
Managerial accounting
ISBN: 978-0471467854
1st edition
Authors: ramji balakrishnan, k. s i varamakrishnan, Geoffrey b. sprin
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