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13 Nov 2019
HW13.pdf math1300 w13pd (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain Use the following definition for area to answer Problems 2 and 3: Definition: The area A of the region S that lies under the graph of the continuous function fis the limit of the sum of the areas of approrimating rectangles: 2. Use the definition of area given above to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 3. (a) Use the definition of area given above to find an expression for the area under the curve 3 from 0 to 1 as a limit. (b) The following formula for the sum of the cubes of the first n integers is proved in Appendix F of your textbook. Use it to evaluate the limit in part (a). +å«"(21)12 1,2433 + a 12
HW13.pdf math1300 w13pd (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain Use the following definition for area to answer Problems 2 and 3: Definition: The area A of the region S that lies under the graph of the continuous function fis the limit of the sum of the areas of approrimating rectangles: 2. Use the definition of area given above to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. 3. (a) Use the definition of area given above to find an expression for the area under the curve 3 from 0 to 1 as a limit. (b) The following formula for the sum of the cubes of the first n integers is proved in Appendix F of your textbook. Use it to evaluate the limit in part (a). +å«"(21)12 1,2433 + a 12
Casey DurganLv2
5 May 2019