1. Definition of function limit
In a certain change process of an independent variable, if the corresponding function value is infinitely close to a certain number, then this certain number is called the limit of the function in this change process.
2. The form of function limit
1. The independent variable tends to a finite value
limit(f,x,a)
limit(f,a)
limit(f)
any of the three
1.1 Example
1.2 MATLAB program
syms x
f=(1-cos(2*x))/(x*sin(x));
limit(f,x,0)或者limit(f,0)或者limit(f)
1.3 Running Results
ans =
2
2. The independent variable tends to infinity
limit(f,x,inf)
limit(f,inf)
Either of two
2.1 Example
2.2 MATLAB program
syms x n
f=2^n*sin(x/2^n);
limit(f,n,inf)或者limit(f,inf)
2.3 Running Results
ans =
real(x) + imag(x)*1i
3. The independent variable tends to the left and right limits
limit(f,x,‘left’)
limit(f,x,‘right’)
3.1 Example
3.2 MATLAB program
syms x
f=x-1;
limit(f,x,0,'left')
syms x
f=x+1;
limit(f,x,0,'right')
3.3 Running results
ans =
-1
ans =
1