Questions about how Mathematica evaluates expressions, tracing evaluation (Trace*), handling expressions in unevaluated form (Hold*, Unevaluated), nonstandard evaluation, etc.

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Define a Plot3D function with custom options [duplicate]

I am trying to define a Plot3D function with custom options, following (this previous SE question), but I'm running into a brick wall. I've narrowed the problem to the following 'toy' code: ...
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How to ContourPlot a Table? [duplicate]

Possible Duplicate: Why is ContourPlot not displaying this curve? Why do I have to put Evaluate[] here I'm trying to plot certain contours of a function $f:\mathbb R^2\to\mathbb R$. What I ...
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Why doesn't Mathematica evaluate this limit?

I am trying to evaluate a few limits in Mathematica, and I can only get it to evaluate them in certain cases. I don't fully understand the evaluation order and when it substitutes numerical values in ...
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Why does the function Evaluate speed up one function by orders of magnitude and another function not at all?

I've got two functions, one sample function (function 1) i've created for demonstartion purposes here, and my actual function. The function Evaluate speeds up the sample function by orders of ...
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Find the value by using FindRoot command [closed]

The equation x^4-3 x^3 = cos(3x)+3 has two real solutions on the interval from -10 to 10. Lets call these two solutions r and s. Use Mathematica's FindRoot command to find r and s. Now let M equal the ...