Question

1) Use finite approximation to estimate the area under the graph of f(x) = x^2 and above the graph of f(x) = 0 from Xo = 0 to Xn= 2 using

i) a lower sum with two rectangles of equal width

ii) a lower sum with four rectangles of equal width

iii) an upper sum with two rectangles of equal width

iv) an upper sum with four rectangles if equal width

2) Use finite approximation to estimate the area under the graph of the function f(x) = 24 -x^2+2x between x= - 4 and x=6 for each of the following cases

a) Using a lower sum with two rectangles of equal width

b) Using a lower sum with four rectangles of equal width

c) Using an upper sum with two rectangles of equal width

d) Using an upper sum with four rectangles if equal width

Answer #1

Use finite approximation to estimate the area under the graph of
f(x)=x2 and above the graph of f(x)=0 from
x0=0 to xn =12 using
i) a lower sum with two rectangles of equal width.
ii) a lower sum with four rectangles of equal width.
iii) an upper sum with two rectangles of equal width.
iv) an upper sum with four rectangles of equal width.
The estimated area using a lower sum with two rectangles of
equal width is ______ square...

Use finite approximations to estimate the area under the graph
of the function f(x) =8−x2+2x between x = −2 and x = 4 for each of
the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

Use finite approximations to estimate the area under the graph
of the function f(x) = 24−x2+2x between x = −4 and x = 6 for each
of the following cases. a. Using a lower sum with two rectangles of
equal width b. Using a lower sum with four rectangles of equal
width c. Using an upper sum with two rectangles of equal width d.
Using an upper sum with four rectangles of equal width

Estimate the area under the graph of f left parenthesis x right
parenthesis equals 5 x cubed f(x)=5x3 between x equals 0 x=0 and x
equals 1 x=1 using each finite approximation below. a. A lower sum
with two rectangles of equal width b. A lower sum with four
rectangles of equal width c. An upper sum with two rectangles of
equal width d. An upper sum with four rectangles of equal width

Use a finite approximation to estimate the area under the graph
of the given function on the stated interval as instructed. 1) f(x)
= x 2 between x = 3 and x = 7 using a left sum with four rectangles
of equal width.

(1 bookmark) Use the midpoint rule to estimate the area under
graph of f(x) =5/x and above the graph of f(x) = 0 from X0 = 1 to
Xn =65 Using two rectangles equal width and four rectangles of
equal width

Use a finite sum to estimate the area under the graph of the
function f(x)=x^2-7 on [-3,7] divided into 5 subintervals and
evaluation the function at the right -end points of the
subinterval.

Estimate the area under the graph of f ( x ) = 1 x + 1 over the
interval [ 3 , 5 ] using two hundred approximating rectangles and
right endpoints
R n =
Repeat the approximation using left endpoints
L n =

(a) Estimate the area under the graph of f(x) = 2/x from x = 1
to x = 2 using four approximating rectangles and right endpoints.
(Round your answer to four decimal places.)
(b) Repeat part (a) using left endpoints. (Round your answer to
four decimal places.)

Estimate to the hundredth the area from 0 to 2 under the graph
of f(x) = e^x - 3 using 4 approximating rectangles and midpoints
endpoints.

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