Question

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

Answer #1

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

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...

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...

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.

For the function f(x) = x, estimate the area of the region
between the graph and the horizontal axis over the interval 0≤x≤4
using a .
a. Riemann Left Sum with eight left rectangles.
b. Riemann Right Sum with eight right rectangles.
c. A good estimate of the area.

(a) Approximate the area of the region beneath the graph of
f(x) =
e−x2,
from x = −1 to x = 1 using (i)
four left rectangles, (ii) four right rectangles, and (iii) four
midpoint rectangles (answer with 3 decimal points).
(b) The actual area, to nine decimal places, of the region
beneath the graph of f(x) =
e−x2 is 1.493648266. Which
of the approximations found in part (a) is the most accurate?

Estimate the area under the curve described by
f(x)=x2+1
between [1, 3] using 8 rectangles. You may define the height of
your rectangles using the left- or right-edge.

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