Dear All

The "pi issue" reminded me of a recent incident in one of my classes
in connection with the introduction of "e".
I asked the class to consider the expression (1+h)^(1/h) for small
values of h.  I was using DERIVE live in the class, and accessed the
simplify, substitute commands to give h different values.  I let h
take the value 10^(-3) then used the approximate operator to get
a nice result.  I then let h take the value 10^(-6) and oops! - not what
I expected - try it and see!
I had to think quickly in order to get the desired result by altering the
working precision.
Of course, LIM((1+h)^(1/h),h,0) simplifies correctly to e WITHOUT
any need to tinker with precision modes as I am sure that my friend
Johann will be able to explain.

Cheers,
            Boz Kempski.
-----Original Message-----
From: Johann Wiesenbauer <[log in to unmask]>
To: [log in to unmask] <[log in to unmask]>
Date: 14 February 2000 09:33
Subject: Re: bugs? pi and solution of an equation


>
>At 05:19 AM 2/14/00 +0100, Berthold Heinrich wrote:
>
>>Can you help me?
>>
>>1. if you approximate pi, you get the wrong number
>>
>>3.14159292035
>>
>>
>>2. If you try to solve the square-root-equation
>>                               10
>>‹(5·x - 56) = ‹(x + 12) - ———————————
>>                           ‹(x + 12)
>>
>>x : Real (0, –)
>>
>>you get the wrong solution x=-13
>>
>>[x = 13, x = -13]
>>
>>Can you help me?
>>
>>Berthold Heinrich
>>
>
>The first question has already been answered by David. The only thing I
>want to supplement is that the assignment
>
>PrecisionDigits := 12
>
>alone will suffice, because the variable NotationDigits gets the same value
>automatically.
>
>As for your second question I would like to point out that (like it or lump
>it!) declaring the domain of variables will not affect subsequent SOLVE
>commands involving those variables (at least not in the way you thought!)
>The declaration of a variable serves a different purpose. For example,
>DERIVE will only simplify the expression sin(n pi) to 0, if you declared n
>as an integer before (which makes sense, doesn't it?)
>
>On the other hand, it's easy to get a vector of all positive solutions of
>your equation by simplifying
>
>select(x>0,x,rhs(solve(sqrt(5x-56)=sqrt(x+12)-10/sqrt(x+12),x)))
>
>There may be other cases though, where things are not that simple.
>
>Cheers, Johann
>
>
>
>
>
>
>
>



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