MaplePrimes - answers and comments on Question, Maple gives limit as undefined but answer is sqrt(2) Why??

not quite

Axel Vogt — Mon, 05 Jul 2010 21:53:38 Z

'limit( x/sqrt(1-cos(x)), x=0,right)': '%'=%;
                                   x            1/2
                     lim    ---------------- = 2
                   x -> 0+  sqrt(1 - cos(x))

'limit( x/sqrt(1-cos(x)), x=0,left)': '%'=%;

                                  x             1/2
                    lim    ---------------- = -2
                  x -> 0-  sqrt(1 - cos(x))

Also never hesitate to plot your task in case of doubts and troubles:

plot( x/sqrt(1-cos(x)), x=-0.1 .. 0.1);

limit

gkokovidis — Mon, 05 Jul 2010 21:55:26 Z

restart:

f:=x/sqrt(1-cos(x));

limit(f,x=0,complex);

From the help files:

If dir is complex, the limit point infinity denotes complex infinity, that is, all infinities in the complex plane. If dir is real, the limit point infinity denotes both positive and negative infinity, and the limit is done bidirectionally. Otherwise, the limit point infinity denotes positive infinity, and -infinity denotes negative infinity.

one-sided

Robert Israel — Mon, 05 Jul 2010 22:01:51 Z

Your answer is correct for the one-sided limit as x -> 0+. In Maple's notation, that would be

limit(x/sqrt(1-cos(x)^2), x = 0, right)

But the one-sided limit as x -> 0- is -sqrt(2), so Maple is correct that the (two-sided) limit is undefined.