Limit of symbolic expression in MATLAB

• Last Updated : 28 Jun, 2021

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 xf = cos(x)/x;disp('f(x) :');disp(f); % Limit of f when x approaches to Infl = 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 xf = 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 xf = 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 xf = 1/(2*x);disp('f(x) :');disp(f); % Left limit of f when x approaches to 0l = 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 xsyms xf = 1/(2*x);disp('f(x) :');disp(f); % Right limit of f when x approaches to 0l = limit(f,x,0,'right');disp("Right limit: ");disp(l);

Output :

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