Question

approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n=4. f(x)=4x+5 from x=4 to x=6

A) use left endpoints

B) use right endpoints

C) average the answers in parts a and b

D) use midpoints

Answer #1

Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4.
f(x)=e^x+1 fromx=-2 to x=2
(a) Use left endpoints.
(b) Use the right endpoints.
(c) Average the answers in parts (a) and (b)
(d) Use midpoints.
The area, approximated using the left endpoints, is
The area, approximated using the right endpoints, is
The average of the answers in parts (a) and (b) is
The area, approximated using the midpoints, is

Approximate the area under the graph of f(x) and above the
x-axis with rectangles, using the following methods with n=4.
f(x)=6x+4 from x=3 to x=5
a) use left endpoints
b)use right endpoints
c) average the answers in parts a and b
d) use midpoints

Approximate the area under f(x) = (x – 2, above the
x-axis, on [2,4] with n = 4 rectangles using the (a) left endpoint,
(b) right endpoint and (c) trapezoidal rule (i.e. the “average”
shortcut). Be sure to include endpoint values and write summation
notation for (a) and (b). Also, on (c), state whether the answer
over- or underestimates the exact area and why.

Estimate the area under the graph of f(x)=x2+4x from x=2 to x=10
using 4 approximating rectangles and left endpoints. Approximation
=

Estimate the area under the graph of f(x)=1/(x+3) over the
interval [−2,1] using ten approximating rectangles and
right endpoints. a=-2,b=1,n=10
Rn=?
Repeat the approximation using left endpoints.
Ln?
Accurate to 4 places.

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 =

Approximate the area under f(x) = sqrt(16-x2) from 0 to 4 using
four rectangles with left endpoints. Is your approximation an
overestimate or an underestimate?

Estimate the area under the graph of
f(x)=1x+1f(x)=1x+1 over the interval [2,7][2,7] using eight
approximating rectangles and right endpoints.
Rn=Rn=
Repeat the approximation using left
endpoints.
Ln=Ln=
Round answers to 4
places. Remember not to round too early in your
calculations.

Estimate the area under the graph of f(x) = 4
cos(x) from x = 0 to x = π/2
using four approximating rectangles and right endpoints. (Round
your answers to four decimal places.)
Repeat with left endpoints.

Estimate the area under the graph of f(x)=x2+3x from x=1 to x=4
using 33 approximating rectangles and left endpoints.
Approximation =

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 15 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 46 minutes ago

asked 50 minutes ago

asked 53 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago