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(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 =  

t(s) 0 0.5 1 1.5 2 2.5 3 v(ft/s) 1.5 2.6 4.5 8.2 9.6 13.9 16.1

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