euler approximation - weird result

Stefan shared this question 3 years ago
Answered

Hi, we had an assignment where we repeatedly calculated 1.1^10, 1.01^100 and so on, to approximate eulers number.


I made a function f(x)=1+10^-x and a function g(x)=10^x and then f^g which should spare me a lot of typing.


But then I saw the graph and it gets really weird after around x=13. The results cannot be true as they start to vary and then jump to a whole different y.


Is this a computational error, an internal rounding problem or some mistake I do not see now?


My geogebra version is 6.0.542.0-win

My windows version is 10.0.17763.737

Comments (2)

photo
1

Good question. I wonder if it has to do with some numerical limitations. I have used other plotter and it has the same problem.

cffee26cbe25000f45dc759a7f545804

photo
2

GeoGebra works to around 15 significant digits so


f(x)=1+10^-x
will give very inaccurate answers the larger x gets and will give exactly 1 after x = 15 or so.

© 2023 International GeoGebra Institute