Limit of symbolic expression in MATLAB

Limits are functions used in calculus, appearing in the definitions of continuity, derivatives, and integrals. The limit of a symbolic expression is defined as the behavior of the symbolic expression at a particular point.

Suppose  As x approaches to infinity (1/x) becomes 0.

Matlab allows users to calculate the limit of a symbolic expression using limit() method. Different syntax of limit() method

• limit(f,var,a)
• limit(f,a)
• limit(f)
• limit(f,var,a,’left’)
• limit(f,var,a,’right’)

limit(f,var,a)

• It returns the limit of function f when var approaches to a.
• 

Example:

Matlab

% MATLAB code for define a %
% symbolic expression f in variable x %
syms x
f = cos(x)/x;
disp('f(x) :');
disp(f);

% Limit of f when x approaches to Inf
l = limit(f,x,Inf);
disp("Limit (x->Inf): ");
disp(l);

Output :

limit(f,a)

It returns the limit of function f when the default variable approaches to a.

Example:

Matlab

% MATLAB code for define a %
% symbolic expression f in variable x %
syms x
f = x^x;
disp('f(x) :');
disp(f);

% Limit of f when default variable(x) %
% approaches to 0 %
l = limit(f,0);
disp("Limit (x->0): ");
disp(l);

Output:

limit(f)

It returns the limit of function f when the default variable approaches 0.

Example:

Matlab

% MATLAB code for define a %
% symbolic expression f in variable x %
syms x
f = tan(x)/x;
disp('f(x) :');
disp(f);

% Limit of f when x approaches to 0 %
l = limit(f);
disp("Limit (x->0): ");
disp(l);

Output :

limit(f,var,a,’left’)

• It returns the left limit of function f when the var approaches a.
• 

Example:

Matlab

% MATLAB code for define a %
% symbolic expression f in variable x %
syms x
f = 1/(2*x);
disp('f(x) :');
disp(f);

% Left limit of f when x approaches to 0
l = limit(f,x,0,'left');
disp("Left limit: ");
disp(l);

Output :

limit(f,var,a,’right’)

• It returns the right limit of function f when the var approaches a
• 

Example:

Matlab

% Define a symbolic expression f in variable x
syms x
f = 1/(2*x);
disp('f(x) :');
disp(f);

% Right limit of f when x approaches to 0
l = limit(f,x,0,'right');
disp("Right limit: ");
disp(l);

Output :