why use limit function goes wrong

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)

Answer 1

[Walter Roberson]

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.

[warnerchang]

however，when you use limit(f,x,inf,'left') instead, you will also get a wrong result: inf

[Walter Roberson]

 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)