Evaluate the Riemann sum for f(x) = 4 -x, 2s x s 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; - 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where %3D i = 1 Xo, X1, X2, X3, X4 and X5 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 2 Step 2 We wish to find L6 (2)[f(x,) + f(xq) + f(x2) + f(x3) + f(x4) + %3D Since xo, X4, X, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following.
Evaluate the Riemann sum for f(x) = 4 -x, 2s x s 14, with six subintervals, taking the sample points to be left endpoints. Step 1 6 We must calculate L6 = F(x; - 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where %3D i = 1 Xo, X1, X2, X3, X4 and X5 represent the left-hand endpoints of six equal sub-intervals of [2, 14]. Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each rectangle will have width Ax = 2 2 Step 2 We wish to find L6 (2)[f(x,) + f(xq) + f(x2) + f(x3) + f(x4) + %3D Since xo, X4, X, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we must have the following.
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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![Evaluate the Riemann sum for f(x) = 4 -x, 2 s xs 14, with six subintervals, taking the sample points to
be left endpoints.
Step 1
6
We must calculate L6 = F(x; _ 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where
i = 1
Xo, X1, X2, X3, X4
represent the left-hand endpoints of six equal sub-intervals of [2, 14].
and
X5
Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each
rectangle will have width Ax =
2
Step 2
We wish to find L6
(2)[f{x,) + f(xq) + f(x2) + f(x3) + f(x4) + f(xg)].
%3D
Since x, X4, X,, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we
must have the following.
Xo = 2
X, =
X2 =
6.
8.
X3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d5901db-f08a-493a-a04d-15d0534348e1%2Fa9097577-76c3-4bf5-bb41-03c502848445%2Fbyah967_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Evaluate the Riemann sum for f(x) = 4 -x, 2 s xs 14, with six subintervals, taking the sample points to
be left endpoints.
Step 1
6
We must calculate L6 = F(x; _ 1) Ax = [f(x,) + f(x,) + f(x,) + f(x3) + f(x4) + f(xg)] Ax, where
i = 1
Xo, X1, X2, X3, X4
represent the left-hand endpoints of six equal sub-intervals of [2, 14].
and
X5
Since we wish to estimate the area over the interval [2, 14] using 6 rectangles of equal widths, then each
rectangle will have width Ax =
2
Step 2
We wish to find L6
(2)[f{x,) + f(xq) + f(x2) + f(x3) + f(x4) + f(xg)].
%3D
Since x, X4, X,, X3, X a, and x, represent the left-hand endpoints of the six sub-intervals of [2, 14], then we
must have the following.
Xo = 2
X, =
X2 =
6.
8.
X3
![X3 = 8 V
X 4
10
%3D
10
X5 = 12
%3D
12
Step 3
Using f(x) = 4 –
we have the following.
L6 = (2)[f(2) + f(4) + f(6) + f(8) + f(10) + f(12)]
%3D
= 2 3 + (2) + (1) + (0) + (-1) + (-2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d5901db-f08a-493a-a04d-15d0534348e1%2Fa9097577-76c3-4bf5-bb41-03c502848445%2Fepkfsve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:X3 = 8 V
X 4
10
%3D
10
X5 = 12
%3D
12
Step 3
Using f(x) = 4 –
we have the following.
L6 = (2)[f(2) + f(4) + f(6) + f(8) + f(10) + f(12)]
%3D
= 2 3 + (2) + (1) + (0) + (-1) + (-2
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