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### Machine precision near zero: not fulfilled?

I am puzzled by the behavior of Mathematica machine precision with numbers approaching zero. This manifests itself, e.g., with FixedPoint and the like. In the ...
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### Why does DSolve return two solutions for my ODE?

I wanted to solve the differential equation: $y’ = (1+2x)\sqrt{y}$ with $y(0) = 1$. It can be done by hand, and to check my answer I typed the following in Mathematica ...
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### Plotting a defined function gives different results from plotting the function directly

Consider the following piece of code: function[t_]:=Exp[-9 t^2]; LogLogPlot[{function[t],Exp[-9 t^2]},{t,.01,100}] I expect the two plots to exactly overlap each ...
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### Change lighting in ChromaticityPlot3D

It looks to me like ChromaticityPlot3D has some default lighting, but unlike most Graphics3D functions the Lighting option doesn't seem to have any effect. However, the documentation states "...
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### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ...
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### DSolve with SetOptions[Solve, Method -> Reduce] Behaving Differently in Ver 11.1.1

With version "11.1.1 for Microsoft Windows (64-bit) (April 18, 2017)", DSolve[{SI'[s] == Sin[PH[s]] , PH'[s] == Sin[SI[s]]/e}, {SI[s], PH[s]}, s] produces the ...
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### Exp of big negative numbers [duplicate]

I noticed that Exp have a strange behaviour with big negative numbers ...
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### Change system options in package

I use Mathematica mostly for numerical calculations, and sometimes the performance of numerical calculations can be greatly improved if the high-precision arithmetic can be switched off by ...
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### Slow exponential evaluation over lists

This question,which is still unanswered, might be relevant because it involves NIntegrate over lists and it also has Exp. In ...
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### Can I force Mathematica to use machine precision? [duplicate]

Some built-in functions (like Exp) give an arbitrary precision result, even when the argument is a machine precision number. Example: ...