MATLAB极限计算

1.1 MATLAB can use the limit command to calculate the limit, the most basic way to use it is to enter the calculated expression. MATLAB will find the limit when the independent variable tends to zero

example 1: f(x)= and g(x)=x.^3+2, calculate that these two equations tend to approach the limit of 3

syms x
f=(2.*x+1)/(x-2)
g=x.^3+2
F1=limit(f,3)
F2=limit(g,3)
输出结果：

next: limit (f+g,3)

output: ans=36

next we verify:

then we calculate:

k=3
limit(k.*f,3)

output: ans=21

let's then verify that the product of the two functions is equal to the product of the respective limits of the two functions:

CALCULATION: F1.*F2

the output is: ans=203

we continue to verify:

 计算：h=f.^g
limit(h,3)

output:

1.2 calculate limf(x), x tends to ∞

we use the syntax to calculate its limit: limit(f, inf)

我们计算式子 

 计算代码：limit(sqrt(x.^2+x)-x,inf)

输出结果：ans=1/2

1.3左极限和右极限

如果存在间断点，那函数在该点的极限不存在。为了处理函数x=a处不连续的情况他，我们定义函数左极限和右极限。左极限定义趋于x从左边趋近于a的极限。

单变量的函数极限：

 

计算式子是否存在

 syms x
f=(x-3)/abs(x-3)
ezplot(f,[-5,5])

输出结果：

a=limit(f,x,3,'left')

a=-1

b=limit(f,x,3,'right')

b=1

两边结果不相等，该式子不成立

 1.4计算：

 代码：syms x
f=sin(x)/x
L=limit(f,x,0)

得到结果：

 1.5计算

 代码：syms x a b
f=x.*(1+a/x).^x.*sin(b/x)
L=limit(f,x,inf)

 输出结果：