Question

write a code please

Problem 1 Write MATLAB programs to find the following sums with for loops. (a) 12 + 22 + 32 + ... ... ... + 10002. (b) 1 –}+*+*+.........-1003 Problem 2 Make two separate plots of the function f(x) = 0.6x5 – 5x3 + 9x + 2; one plot for -4 < x < 4, and -2.7 < x < 2.7. Plot by creating vectors.

Answer 1

PROBLEM 1

First series is pretty straightforward to implement

For the second series

First term is $\frac{-1^{n}}{2n+1}$ = 1 for n = 0

Second term is $\frac{-1^{n}}{2n+1}$ = -1/3 for n = 1

Third term is $\frac{-1^{n}}{2n+1}$ = 1/5 for n = 2

and so on

for the last term will be for n =501

MATLAB script for the series

clc;
close all;

%%% The first series
sum1 = 0;
for i = 1:10
sum1 = i^2 + sum1;
end
%%% Display the sum in command window
fprintf('The sum of 1st series is %d \n',sum1);

%%% The second series
sum2 = 0;
for n = 0:501
sum2 = ((-1)^n)/(2*n +1) + sum2;
end
%%% Display the sum in command window
fprintf('The sum of 2nd series is %f \n',sum2);

Command line output

Command Window The sum of 1st series is 333833500 The sum of 2nd series is 0.784900 fx >>

PROBLEM 2

For the vector plot, define x between -4 and 4

Vector (function fx) is defined using dot operators as shown in the script below

The plot for -2.7<= x <= 2.7 is obtained by using MATLAB xlim function

MATLAB script

x = linspace(-4,4);
%%% Creates vector x with 100 equidistant points between -4 and 4
fx = 0.6.*x.^5 - 5.*x.^3 + 9.*x +2;
%%% Defines vector fx using dot operators

figure(1)
%%% Plot fx for x between -4 and 4
plot(x,fx);
grid on

figure(2)
%%% Plot fx for x between -2.7 and 2.7, limits set by xlim function
plot(x,fx);
hold on
grid on
xlim([-2.7 2.7]);

Plots

-300 / -400 L -4 -3 - 2 1 0 1 2 3 4

--15 - -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5