Bug?

Adri vanderMeer van der Meer — Wed, 07 Nov 2012 18:54:17 Z

The function is not defined at x=1 and at x=-1 because of a division by zero:

restart;
f := x -> ((1/(1-x^2))^(1/2))*(sin((1-x)^(1/2))):
f(1);
Error, (in f) numeric exception: division by zero
limit( f(x), x=1 );
                           undefined

The discontinuity cannot be removed

 limit( f(x), x=1 );
                           undefined
limit( f(x), x=1, left );
                            1  (1/2)
                            - 2     
                            2       
limit( f(x), x=1, right );
                             1  (1/2)
                           - - 2     
                             2       
plot(f(x), x=-2..2, discont=true );

As you see, the graph is not plotted for x ≤ -1

 limit( f(x), x=-1, right );
                            infinity
f(-2);
                     1    (1/2)    / (1/2)\
                     - I 3      sin\3     /
                     3

This is not a real number.
But if we define

 h := x -> sin(sqrt(1-x))/sqrt(1-x^2):
limit( h(x), x=1);
                            1  (1/2)
                            - 2     
                            2       
plot(h,-2..2);

This function seems to be continuous at x=1!
There seems to be a bug in the evaluation of f(x) for x ≥ 1:

 p := sin( I*sqrt(x-1) );
                            /       (1/2)\
                      I sinh\(x - 1)     /
q := 1/(I*(x^2-1)^(1/2));
                                I       
                        - --------------
                                   (1/2)
                          /      2\     
                          \-1 + x /     
p*q;
                           /       (1/2)\
                       sinh\(x - 1)     /
                       ------------------
                                  (1/2)  
                         /      2\       
                         \-1 + x /

This is positive if x > 1

eldkey.mw

Branch

Preben Alsholm — Wed, 07 Nov 2012 20:22:53 Z

Maple takes the principal branch of the square root.

Thus if we define s1 and s2 as

s1:=x->1/sqrt(1-x^2);
s2:=x->sqrt(1/(1-x^2));
#then there will be a difference between the following two:
s1(2);
s2(2);
#As is also seen here
1/sqrt(-3);
sqrt(-1/3);

think you !

eldkey — Thu, 08 Nov 2012 03:31:24 Z

Tihnk you Adri vanderMeer van der Meer , very much and think you Preben Alsholm for your explanations , i was very lost on this problem!

MaplePrimes - answers and comments on Question, Why i am not getting it ?!

Bug?

Branch

think you !