Another oddity, integral in home
12-02-2016, 07:00 PM
Post: #8
 Jan_D Member Posts: 69 Joined: Nov 2016
RE: Another oddity, integral in home
It is interesting to compare the results of HP Prime with the results of Geogebra.
We do this for the function we are talking about, let’s call it F(x), not for the integral.

Interesting about Geogebra is that it can calculate expressions with a precision of 100 significant digits, by using its cas command: Numeric[F(x),100].

So we can assume that the results of Geogebra are reliable.

We are also interested in the Taylor expansion of F (series or taylor command) and let its highest order term be (x^9)*√x.
We call this function T(x).

Now we calculate F(0.1) and T(0.1) in the Prime’s CAS.
This gives:
F(0.1)=0.792222219896
T(0.1)=0.792222219897. Geogebra gives Fgeo=0.79222221989709.........

So it is interesting to see that even for x=0.1 the Taylor expansion on the Prime is accurate until the last digit and even a bit more accurate than the direct calculation of F(0.1).

It is not surprising that this is not so anymore for F(1) and T(1).
In that case F(1) is completely precise, and T(1) much less.

Let’s see what the results are for x=1E-4.
Then:
F(1E-4)=25.0000020685
T(1E-4)=25.0000000521 and Fgeo=25.000000052083.......

Let’s finaly see what the results are for x=1E-12.
Then:
F(1E-12)=0.
T(1E-12)=250000. and Fgeo=250000.00000000000000.....

Thus we observe that the Taylor expansion keeps being completely precise, whereas F(x) is getting less and less precise.

So we can conclude that the power of using a Taylor expansion is indeed impressive.

I have firmware version 8151.
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 Messages In This Thread Another oddity, integral in home - lrdheat - 11-27-2016, 06:54 PM RE: Another oddity, integral in home - lrdheat - 11-27-2016, 07:21 PM RE: Another oddity, integral in home - compsystems - 11-27-2016, 10:19 PM RE: Another oddity, integral in home - Marcel - 11-27-2016, 11:37 PM RE: Another oddity, integral in home - lrdheat - 11-28-2016, 04:37 AM RE: Another oddity, integral in home - Dirk.nl - 11-28-2016, 05:30 AM RE: Another oddity, integral in home - parisse - 11-28-2016, 06:59 AM RE: Another oddity, integral in home - Jan_D - 12-02-2016 07:00 PM

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