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(a) The rectangles in the graph on the left illustrate a left endpoint sum for f

ID: 2894525 • Letter: #

Question

(a) The rectangles in the graph on the left illustrate a left endpoint sum for f(x) on the interval 3 lessthanorequalto x lessthanorequalto 5. The value of these left endpoint , and it is an the area of the region enclosed by y = f(x), x axis and the vertical lines x = 3 and x = 5. (b) The rectangles in the graph on the right illustrate a night endpoint sum for f(x) on the intervals 3 lessthanorequalto x lessthanorequalto 5. The value of the night endpoint sum is , and it is an the area of the region enclosed by y = f(x). the x-axis and the vertical lines x = 3and x = 5.

Explanation / Answer

given f(x)=12/x

a=3, b=5, number of subintervals n=4 , length of each subinterval x =(5-3)/4=0.5

a)

left endpoint reimann sum =x(f(3)+f(3.5)+f(4)+f(4.5))

left endpoint reimann sum =0.5*((12/3)+(12/3.5)+(12/4)+(12/4.5))

left endpoint reimann sum =275/42

it is an overestimate

b)

right endpoint reimann sum =x(f(3.5)+f(4)+f(4.5)+f(5))

right endpoint reimann sum =0.5*((12/3.5)+(12/4)+(12/4.5)+(12/5))

right endpoint reimann sum =1207/210

it is an undrestimate

if fractions are not accepted enter the decimals 6.5476,5.7476