Speedometer readings for a motorcycle at 12-second intervals are given in the table
t (s) 012 2436 48 60
V (ft/s) 32 2725 2124 27
(A) Estimate the distance traveled by the motorcycle during this time period using a left-hand sum with n-5 ft
(B) Give another estimate using a right-hand sum with n=5. ft
(C) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.
I (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.
II (a) and (b) are neither lower nor upper estimates since v is neither a strictly increasing nor strictly decreasing function of t
III (b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.