# why use limit function goes wrong

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warnerchang el 9 de Abr. de 2022
Comentada: Walter Roberson el 9 de Abr. de 2022
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 el 9 de Abr. de 2022
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.
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warnerchang el 9 de Abr. de 2022
however，when you use limit(f,x,inf,'left') instead, you will also get a wrong result: inf
Walter Roberson el 9 de Abr. de 2022
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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