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# Consider the following.

Consider the following.
[graph image is in attached file]
(a) Use six rectangles to find estimates of each type for the area under the given graph of f from x = 0 to x = 48.
(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?
M6
R6
L6

Solution:
(a) (i) (ii) (iii) (b) Since f is decreasing, we obtain an overestimate by using left endpoints; that is,
(c) Since f is decreasing, we obtain an underestimate by using right endpoints;...

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