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 :