Question

I AM ADDING THE f FUNCTION GIVEN IN PROBLEM 9.1 ANY HELP IS APPRECIATED PLEASE THANK YOU

For N 0, 1,2, and 3, expand and calculate the value of where - n + 1 ann22 "

Answer 1

$Editor CUsers Vaio\Documents MATLAB\prob19.m 唱唱 - 1.0 + 1.1 % 0, f=5 ; %assigning initilial value to f so as to start the loop h-input (\nEnter the value of N ); assigning user input value to variable N for n=1:N %starting loop from n-1 incrementing to N by 1 every time f-1+((n+1 ) / (n°2+2))*cos (pi*n); %defining the function in terms of n end fprintf(The value of f for N equal to %d is %0.10f\n,N, f) %printing the results on screen :: primey.m × prob19.m x Command Window で Command History New to MATLAB? Watch this Video, see Demos, or read Getting Started Enter the value of N 0 The value of f for N equal to 0 is 5.0000000000 Enter the value of N 1 The value of f for N equal to 1 is 4.3333333333 Enter the value of N 2 The value of f for N equal to 2 is 4.8333333333 Enter the value of N 3 The value of f for N equal to 3 is 4.4696969697 Enter the value of N 100 The value of f for N equal to 100 is 4.6302481157 兵>>$ cos(pi)=-1 and cos(2pi)=1. Since period of cos function is 2pi, for every odd Odd value of n, we'll get -1 and for every even value, we'll get +1. The value of (n+1)/(n^2+2) goes on increasing with every n value.

Initially, at n=1, the value will be subtracted from 5, so we have 4.333 as result.

At n=2, even though the value of cos is positive, it will be added to initially calculated value 4.333. So we see a small increment in it and the answer is 4.833

At, n=3, again some value will be subtracted, since cos(3pi)=-1. So the result will be a lesser value than 4.833 but not as low as 4.333 since some value was added to it in the previous step.

So the results do make sense.

CODE

f=5; %assigning initilial value to f so as to start the loop
N=input('\nEnter the value of N '); %assigning user input value to variable N
for n=1:N %starting loop from n=1 incrementing to N by 1 every time
f=f+((n+1)/(n^2+2))*cos(pi*n); %defining the function in terms of n
end
fprintf('The value of f for N equal to %d is %0.10f\n',N,f) %printing the results on screen