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一：符号表达式expr对自变量x在a处的极限：limit(expr,x,a)

 

二：符号表达式expr对自变量x在a处的左极限：limit(expr,x,a,'left')

三：符号表达式expr对自变量x在a处的右极限：limit(expr,x,a,'right')

 

limit(expr,x,a)
limit(expr,a)
limit(expr)
limit(expr,x,a,'left')
limit(expr,x,a,'right')

Description

limit(expr,x,a) computes bidirectional limit of the symbolic expression expr when x approaches a.

limit(expr,a) computes bidirectional limit of the symbolic expression expr when the default variable approaches a.

limit(expr) computes bidirectional limit of the symbolic expression expr when the default variable approaches 0.

limit(expr,x,a,'left') computes the limit of the symbolic expression expr when x approaches a from the left.

limit(expr,x,a,'right') computes the limit of the symbolic expression expr when x approaches a from the right.

Examples

Compute bidirectional limits for the following expressions:

syms x h
limit(sin(x)/x)
limit((sin(x + h) - sin(x))/h, h, 0)
ans =
1
 
ans =
cos(x)
Compute the limits from the left and right for the following expressions:

syms x
limit(1/x, x, 0, 'right')
limit(1/x, x, 0, 'left')
ans =
Inf
 
ans =
-Inf
Compute the limit for the functions presented as elements of a vector:

syms x a
v = [(1 + a/x)^x, exp(-x)];
limit(v, x, inf)
ans =
[ exp(a), 0]

 

 

 

 

 

 

 

 

 

 

 

 

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