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CALCULUS - LAB ASSIGNMENT 1
1. PARAMETRIC PLOTTING
clc
clear all
close all
t = linspace(0, 2*pi,20);
x = 3+2*cos(t);
y = 4+2*sin(t);
plot(x,y,'k-*')
xlabel('x(m)')
ylabel('y(m)')
title('graph of (x-1)^2+(y-3)^2=4')
legend('(x-1)^2+(y-3)^2=4')
2. MULTIPLE PLOTS IN A FIGURE WINDOW (USING COMMAND HOLD ON)
clc
clear all
close all
x = linspace(0,1)
plot(x,x.^2,'r*')
hold on
plot(x,sin(x),'g.')
plot(x,exp(x),'m+')
legend('x^2','sin(x)','exp(x)')
3. MULTIPLE GRAPHS IN A FIGURE WINDOW BY USING SUBPLOT
clc
clear all
close all
x=0:0.1:2*pi;
subplot(2,2,1)
plot(x,sin(x));
subplot(2,2,2)
plot(x,cos(x),'r-*');
subplot(2,2,3)
plot(x,exp(-x),'go')
subplot(2,2,4);
plot(x,sin(3*x),'ms')
2
3. GRAPH OF A CURVE THROUGH EZPLOT COMMAND
clc
clear all
syms x% Declaring the parameters as a symbolic object
f=sin(2*x)+cos(3*x)
figure(1)
ezplot(f)
figure(2)
ezplot(f,[0,3])
4. GRAPH OF A CURVE AND ITS TANGENT LINE IN THE
NEIGHBOURHOOD D OF A POINT.
syms x
%y=input('enter the function f in terms of x:')% Example, Try the
function y=x^2-2*x;
y=x^2-2*x;
%x1 = input('Enter x value at which tangent : '); % Example, Try
the point x1 = 2
x1=2;
D=[x1-2 x1+2]% Region about x1 (or Neighbourhood of x1)
ezplot(y,D) % graph of the curve in D
hold on
%Equation of the tangent line passing through x1.
yd = diff(y,x); % Differentiation in MATLAB
slope = subs(yd,x,x1); % Finding the slope at x1
y1 = subs(y,x,x1); % Finding the value of the function at the
given point
plot(x1,y1,'ko') % plot the point
Tgt_line = slope*(x-x1)+y1 % Tangent Line Equation at the given
point
h = ezplot(Tgt_line,D); % Plotting the Tangent Line
set(h,'color','r')
1) Find the equation of tangent to the curve y = 2 x at (1,2).
2) Find the equation of tangent to the curve
3 y = x at (-2,-8).
5. EXTREMA OF A SINGLE VARIABLE FUNCTION.
syms x real
f= input('Enter the function f(x):');
fx= diff(f,x)
c = solve(fx)
3
cmin = min(double(c));
cmax = max(double(c));
ezplot(f,[cmin-2,cmax+2])
hold on
fxx= diff(fx,x)
for i = 1:1:size(c)
T1 = subs(fxx, x ,c(i) );
T3= subs(f, x, c(i));
if (double(T1)==0)
sprintf('The point x is %d inflexion point',double (c(i)))
else
if (double(T1) < 0)
sprintf('The maximum point x is %d', double(c(i)))
sprintf('The value of the function is %d', double (T3))
else
sprintf('The minimum point x is %d', double(c(i)))
sprintf('The value of the function is %d', double (T3))
end
end
plot(double(c(i)), double(T3), 'r*', 'markersize', 15);
end
pause
h=ezplot(fx,[cmin-2,cmax+2])
set(h,'color','r')
hold on
pause
e=ezplot(fxx,[cmin-4,cmax+4])
set(e,'color','g')
hold off
Practice Problems:
1. An open-top box is to be made by cutting small congruent squares from the comers of a 12-in.-by-12-in. sheet of tin and bending up the sides. How large should the squares cut from the corners be to make the box hold as much as possible?
4
.
5
2. A rectangle is to be inscribed in a semicircle of radius 2. What is the largest area the rectangle can have, and what are its dimensions?
Length :2x, Height: Area: 2x. A(x)= 2x.