2A) If this function were to be rotated around the horizontal axis in three dimensions, the resulting function would look like the function z = f(x,y) written below. Use fsurf to plot both the positive and negative parts of this multivariable function on the same set of axes using hold on. Use the indicated ranges of values of x and y below for the domain in the xy-plane (figure 1). z = ± √(f(x))² - y² - 1.1 ≤ y ≤ 1.1. 2B) Write clear variables on a line in your script after your answers for 2A, then proceed to the following problem. Consider f(x) from above over the interval [ π/(b + 1), (d + 30)/6]. You are going to find the volume of the solid formed by rotating this function around the x-axis by using MATLAB operations. Use a for loop combined with a sum command to get a left-hand estimate and a right-hand estimate of the volume of the solid (using the washer method). Assume that you will have 25 subrectangles for both estimates. Compute the average of the left and right sums in MATLAB and declare your result P2B. TT b + 1 ≤x≤ 10 2C) Write clear variables on a line in your script after your answers for 2B, then proceed to the following problem. Consider f(x) from above over the same interval [n/(b + 1), (d + 30)/6]. You are going to find the volume of the solid formed by rotating this function around the x-axis again by using MATLAB operations; this time, use int and vpa together to get a numerical approximation. Declare your result P2C.
2A) If this function were to be rotated around the horizontal axis in three dimensions, the resulting function would look like the function z = f(x,y) written below. Use fsurf to plot both the positive and negative parts of this multivariable function on the same set of axes using hold on. Use the indicated ranges of values of x and y below for the domain in the xy-plane (figure 1). z = ± √(f(x))² - y² - 1.1 ≤ y ≤ 1.1. 2B) Write clear variables on a line in your script after your answers for 2A, then proceed to the following problem. Consider f(x) from above over the interval [ π/(b + 1), (d + 30)/6]. You are going to find the volume of the solid formed by rotating this function around the x-axis by using MATLAB operations. Use a for loop combined with a sum command to get a left-hand estimate and a right-hand estimate of the volume of the solid (using the washer method). Assume that you will have 25 subrectangles for both estimates. Compute the average of the left and right sums in MATLAB and declare your result P2B. TT b + 1 ≤x≤ 10 2C) Write clear variables on a line in your script after your answers for 2B, then proceed to the following problem. Consider f(x) from above over the same interval [n/(b + 1), (d + 30)/6]. You are going to find the volume of the solid formed by rotating this function around the x-axis again by using MATLAB operations; this time, use int and vpa together to get a numerical approximation. Declare your result P2C.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
a=3 b=7 c=7 d=17
Transcribed Image Text:The second component of this project is to graph and find the volume of a specific solid of revolution using the
operations learned in the first component of this project. Your goals will include plotting a rotated curve that
generates a surface in three dimensions and evaluating the volume of the interior of that surface by using several
of the methods discussed in the first part of this project. The function you will working with is widely used in
optics and digital signal processing and is called the sinc function. It is given below and randomized as usual.
f(x)
=
(a + c
(a + c + 4) sin((b + 1)x)
(b + 1)x
4
![2A) If this function were to be rotated around the horizontal axis in three dimensions, the resulting function would
look like the function z = f(x,y) written below. Use fsurf to plot both the positive and negative parts of this
multivariable function on the same set of axes using hold on. Use the indicated ranges of values of x and y below
for the domain in the xy-plane (figure 1).
z = ± √(f(x))² - y²
- 1.1 ≤ y ≤ 1.1.
2B) Write clear variables on a line in your script after your answers for 2A, then proceed to the following
problem. Consider f(x) from above over the interval [ п/(b + 1), (d + 30)/6 ]. You are going to find the
volume of the solid formed by rotating this function around the x-axis by using MATLAB operations. Use a for
loop combined with a sum command to get a left-hand estimate and a right-hand estimate of the volume of the
solid (using the washer method). Assume that you will have 25 subrectangles for both estimates. Compute the
average of the left and right sums in MATLAB and declare your result P2B.
π
b + 1
≤x≤ 10
2C) Write clear variables on a line in your script after your answers for 2B, then proceed to the following
problem. Consider f(x) from above over the same interval [ π/(b + 1), (d + 30)/6]. You are going to find
the volume of the solid formed by rotating this function around the x-axis again by using MATLAB operations;
this time, use int and vpa together to get a numerical approximation. Declare your result P2C.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe192fe17-3d15-43f1-9083-5e30f93ccdf8%2F76736b1a-423d-4d17-890e-467c4483313c%2F8exr9cq_processed.png&w=3840&q=75)
Transcribed Image Text:2A) If this function were to be rotated around the horizontal axis in three dimensions, the resulting function would
look like the function z = f(x,y) written below. Use fsurf to plot both the positive and negative parts of this
multivariable function on the same set of axes using hold on. Use the indicated ranges of values of x and y below
for the domain in the xy-plane (figure 1).
z = ± √(f(x))² - y²
- 1.1 ≤ y ≤ 1.1.
2B) Write clear variables on a line in your script after your answers for 2A, then proceed to the following
problem. Consider f(x) from above over the interval [ п/(b + 1), (d + 30)/6 ]. You are going to find the
volume of the solid formed by rotating this function around the x-axis by using MATLAB operations. Use a for
loop combined with a sum command to get a left-hand estimate and a right-hand estimate of the volume of the
solid (using the washer method). Assume that you will have 25 subrectangles for both estimates. Compute the
average of the left and right sums in MATLAB and declare your result P2B.
π
b + 1
≤x≤ 10
2C) Write clear variables on a line in your script after your answers for 2B, then proceed to the following
problem. Consider f(x) from above over the same interval [ π/(b + 1), (d + 30)/6]. You are going to find
the volume of the solid formed by rotating this function around the x-axis again by using MATLAB operations;
this time, use int and vpa together to get a numerical approximation. Declare your result P2C.
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