An incorrect evaluation of a function at a point...

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As a new user of Maple (Maple 2015), I defined the function:

f:=x->(1+1/x)^x

As x->infinity, f(x) increases monotonically to e, as is known.

In financial applications, this function and related functions are often used to show that periodic compounding converges to continuous compounding as the number of compounding periods grows larger.

However, for certain large values of x, f(x) evaluates to functional values larger than e.  For example:

f(x)|x=31536000. evaluates to 2.74327....

which is greater than e=2.71828...

Also notice that is(f(31536000.)>e) returns true.

This incorrect evaluation makes it difficult to demonstrate to students the principles of and relationship between periodic compounding and continuous compounding.

Some other CAS (Mathematica and HP Prime) evaluate the function correctly while TI Nspire also evaluates the function incorrectly.

The following file demonstrates this behavior of Maple 2015:

20160705_example_of_function_evaluation_issue.mw

Can anyone share any insight to this issue or any errors that I am making.

how to avoid round off errors ?...

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i do not want maple to round off some terms , for example 1.7777777777 which is rounded off 1.7777777778 . i do not want maple to round off the result,what should i do ?

session dependent results

by: Maple

Perhaps you have heard the terms "ordering difference" or "session dependent" applied to results of some Maple computation. It used to get heard more often back before Maple 12, when elements of sets in Maple were ordered according to address.

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