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Calculus

[New] Problem : compute the limit of when n goes to infinity, and the limit of when x goes to zero.

>> limit((1+1/n)^n,n=infinity);

                                     E

>> limit((1-cos(x))/x^2,x=0);

                                    1/2

It should be noted that the limit functions of MuPAD implements the best known algorithm to this date. It is based on the concept of most-rapidly-varying subexpressions (MRV), and a comparison made by Dominik Gruntz on 19 exp-log expressions [3] showed that the algorithms implemented in other computer algebra systems (except Maple and MuPAD) fail on many examples, and even return wrong values !



Andre Heck
Sun Apr 23 10:32:10 MDT 1995