why use limit function goes wrong

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warnerchang
warnerchang 2022년 4월 9일
댓글: Walter Roberson 2022년 4월 9일
syms x
f=(2/pi*atan(x))^x;
limit(f,x,inf,'right')
Prompt:Inconsistent limit direction.
however,I tried to transform the f and used limit function to get the limit. It has a result.
% y = 1 - 2 / pi * atan( x ); % transformation,x -> ∞ ,y -> 0
% x = tan( pi/2 - pi/2 * y ); % equation
syms y
f = ( 1 - y ) .^ ( tan( pi/2 - pi/2 * y ) )
limit( f, y, 0 )
ans =
exp(-2/pi)

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Walter Roberson
Walter Roberson 2022년 4월 9일
Asking for the "right" limit means that you want the limit from above. As you are asking for the limit at infinity, that would be asking for the limit from "above" infinity. However, MATLAB does not have any support for transfinite numbers.
  댓글 수: 2
warnerchang
warnerchang 2022년 4월 9일
however,when you use limit(f,x,inf,'left') instead, you will also get a wrong result: inf
Walter Roberson
Walter Roberson 2022년 4월 9일
syms x
f=(2/sym(pi)*atan(x))^x;
limit(f,x,inf,'left')
MATLAB does not identify 2/pi (numeric double precision) as being the same as 1/(π/2) (the symbolic limit)

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