(A) Estimate the area under the graph of f(x)=59x2 from x=2 to x=4 using three a
ID: 2855520 • Letter: #
Question
(A) Estimate the area under the graph of f(x)=59x2 from x=2 to x=4 using three approximating rectangles and right endpoints.
Estimate =
(B) Repeat part (A) using left endpoints.
2/The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table:
(a) Find a lower estimate for the distance that she traveled during these three seconds.
(b) Find an upper estimate for the distance that she traveled during these three seconds.
Estimate =
(C) Repeat part (A) using midpoints.
Estimate =
3/The value of the limit
limni=1n6n2+6in
is equal to the area below the graph of a function f(x) on an interval [A,B]. Find f, A, and B. (Do not evaluate the limit.)
f(x) =
A = (use A=0)
B =
Explanation / Answer
1)f(x)=59x2
x..............-2.............0............2.............4
f(x)..........55.............59..........55...........43
(A)
a=-2,b=4,n=3
x =(b-a)/n =(4-(-2))/3 =2
area under the graph of from x=2 to x=4 using three approximating rectangles and right endpoints.
=x[f(0)+f(2)+f(4)]
=2[59+55+43]
=314
Estimate = 314
(B) using left endpoints.
x[f(-2)+f(0)+f(2)]
=2[55+59+55]
=338
Estimate = 338
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