I ran into a bug when I prepared a worksheet with Maxima 5.19 that
should be used to explore equivalence or nonequivalence of several
definitions of the derivative. Three forms of the difference quotient
are defined:
diffquot(f,x,h):=(f(x+h)-f(x))/h;
diffquotL(f,x,h):=(f(x)-f(x-h))/h;
diffquotB(f,x,h):=(f(x+h)-f(x-h))/(2*h);
The error occurs with the following demo function:
f3(x):=sin(3*x-5);
Only the last two of the following commands yield the correct result,
the first gives infinity.
limit(diffquot(f3,x,h),h,0);
limit(diffquotL(f3,x,h),h,0);
limit(diffquotB(f3,x,h),h,0);
Reinhard Oldenburg