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# Calculs hw

Consider the following. (a) Use six rectangles to find estimates of each type for the area under the given graph of f from x = 0 to x = 24. (i) Sample points are left endpoints. L6 = (ii) Sample points are right endpoints. R6 = (iii) Sample points are midpoints. M6 = (b) Is L6 an underestimate or overestimate of the true area? overestimate underestimate     (c) Is R6 an underestimate or overestimate of the true area? overestimate underestimate     (d) Which of the numbers gives the best estimate? R6 M6     L6 2-Do the following. Estimate the area under the graph of f(x) = 2 cos(x) from x = 0 to x = p/2. (Round the answer to four decimal places.) (a)  Use four approximating rectangles and right endpoints. R4 = Is your estimate an underestimate or an overestimate? underestimate overestimate     (b)  Use four approximating rectangles and left endpoints. L4 = Is your estimate an underestimate or an overestimate? underestimate overestimate     3-Speedometer readings for a motorcycle at 12-second intervals are given in the table. t (s)01224364860v (ft/s)322725222427(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals. ft (b) Give another estimate using the velocities at the end of the time periods. ft (c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain. (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t. (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.     (a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t. 4-Oil leaked from a tank at a rate of r(t) liters per hour. The rate decreased as time passed, and values of the rate at two hour time intervals are shown in the table. Find lower and upper estimates for the total amount of oil that leaked out. V˜L (lower estimate)V˜L...

Apr 25 2020 View more View Less

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