why use limit function goes wrong

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warnerchang
warnerchang 2022-4-9
评论： Walter Roberson 2022-4-9
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 2022-4-9
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.
  2 个评论
warnerchang
warnerchang 2022-4-9
however，when you use limit(f,x,inf,'left') instead, you will also get a wrong result: inf
Walter Roberson
Walter Roberson 2022-4-9
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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