why use limit function goes wrong

5 vues (au cours des 30 derniers jours)
warnerchang
warnerchang le 9 Avr 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)

Réponse acceptée

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