Help writing a MATLAB program please. for problem 3.2. Thanks f(x)=(1+x)^1/3 = 1
ID: 3677433 • Letter: H
Question
Help writing a MATLAB program please. for problem 3.2. Thanks
f(x)=(1+x)^1/3 = 1+1/3 x - 1.2/3.6 x^2 + 1.2.5/3.6.9 x^3 - 1.2.5.8/3.6.9.12 x^4 +... The binomial expansion for (1 + x)n, where n is an integer, is as follows(1+x)^n, where n is an integer, is as follows: (1+x)^n = 1+nx+ n(n-1)x^2/2! + n(n-1)(n-2)x^3/3! + .... +n(n-1)(n-2)...(n-r+2)x^r-1/(r-1)! +...+ x^n Construct a MATLAB program that will evaluate (1 + x)^n by both the series and by an arithmetic statement for n = 10 and 1.0 x 10.0 in steps of 0.5. Print out the results in a table as shown in Table P3.2..3 This project is axmodification of Project P2.2 Instead of making the program interactive, enter the following altitudes, z2, at which the atmospheric are to be determined by linear interpolation usingExplanation / Answer
1)matlab program
py=1;
y=ones(1,20);
i=1;
for x=1.0:0.5:10.0
for k=1:10;
py=py*((1/3)-(k-1))*(x/k);
y(1,i)=y(1,i)+py;
end
x
y(1,i)
i=i+1;
end
output:
x =
1
ans =
1.2545
x =
1.5000
ans =
1.0003
x =
2
ans =
0.9435
x =
2.5000
ans =
8.1580
x =
3
ans =
-5.2422e+003
x =
3.5000
ans =
1.7618e+007
x =
4
ans =
-2.2288e+011
x =
4.5000
ans =
9.0972e+015
x =
5
ans =
-1.0601e+021
x =
5.5000
ans =
3.1931e+026
x =
6
ans =
-2.2900e+032
x =
6.5000
ans =
3.6491e+038
x =
7
ans =
-1.2180e+045
x =
7.5000
ans =
8.0945e+051
x =
8
ans =
-1.0245e+059
x =
8.5000
ans =
2.3755e+066
x =
9
ans =
-9.7471e+073
x =
9.5000
ans =
6.8632e+081
x =
10
ans =
-8.0666e+089
2)matlab program:
px=1;
temp=1;
y=ones(1,19);
i=1;
n=10;
X=1.0:0.5:10.0;
for x=1.0:0.5:10.0
for r=0:9;
px=(px*(n-r)*x)/factorial(r+1);
y(i)=temp+px;
temp=y(i);
end
i=i+1;
end
A =[X;y];
%store the T,h in table formate in a file
fileID = fopen('exp.txt','w');
fprintf(fileID,'%6s %12s ','x','(1+x)^n');
fprintf(fileID,'%6.2f %8.4f ',A);
fclose(fileID);
%view the content of a file
type exp.txt
output:
x (1+x)^n
1.00 134.3811
1.50 134.3811
2.00 134.3811
2.50 134.3811
3.00 134.3811
3.50 134.3811
4.00 134.3811
4.50 134.3811
5.00 134.3811
5.50 134.3811
6.00 134.3811
6.50 134.3811
7.00 134.3811
7.50 134.3811
8.00 134.3811
8.50 134.3811
9.00 134.3811
9.50 134.3811
10.00 134.3811
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