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For example, if the functions were named OverTake, then: OverTake[{1, 2}, 5] (* {1, 2, 1, 2, 1} *) (This would be a direct analog of the take functions in the array-processing languages APL and J.) …

For a visual, animated, description of basic behavior of such functions, I recommend: http://reference.wolfram.com/legacy/flash/ (You may want to turn on your computer's sound.) …

I frequently encounter the situation where I have a function of two real variables defined, e.g.: f[x_, y_] := 9 - x^2 - y^2 But then I need to feed into f not just two numbers but rather a pair, i …

To implement "Hero's Method" for approximating $\sqrt{c}$, one iterates the function (x + c/x)/2 for a given number c (e.g., 2) starting with some initial value of x. This can be implemented by defini …

First, a basic mistake: in Mathematica, the natural log base is entered as E (or as Esc e Esc), and not plain e. And many folks prefer Exp[x] to E^x. Also, your lines f[1];, f[2];, etc., since they e …

Note that there is another, newer, way to store definitions that may suit your purposes: to store then as local objects (or even as cloud objects), then retrieve them when needed. I'll illustrate with …

How can the actual definition of a function be hidden from a user? I want the user of a notebook to be able to evaluate a real-valued function f of a real variable at any particular numeric input yet …

a = 30; f[x_] := Sqrt[2/a] (3/5 Sin[2 \[Pi] x/a] + 4/5 Sin [(9 \[Pi] x)/a]) Plot[f[x], {x, 0, a}, AxesLabel -> {x, "f(x)"}, PlotStyle -> {Black, Dashed}] Note that you forgot the closing ) in th …

As noted, you didn't show a Mathematica definition of f. Moreover, the definitions of traj is incorrect, and the syntax of Manipulate is wrong. Here's a corrected, complete version: f[x_, a_] := a - …

Perhaps you mean something like this: f[{x1_, x2_}, {y1_, y2_}] := x1 y2 - x2 y1 Reduce[ForAll[{x1, x2, y1, y2}, {x1, x2}.{y1, y2} <= f[{x1, x2}, {y1, y2}]]]

For the record... no function, whether defined by SetDelayed (:=) or Set (=) expliclty or by constructing a pure function (using # and &) is needed. To wit: -800 {3, 7} + 12000 {9600,6400}

Use Map, abbreviated /@. For example: lis = {4, 5/2, 3., 6/3, Pi}; IntegerQ /@ lis (* or Map[IntegerQ, lis] *) (* {True, False, False, True, False} *)

output from dict = Nearest[WordData[]] is a NearestFunction object -- a function that may then be evaluated at an input such as: dict["eleephannt"] {elephant} How can one determine which other functions …

I don't think this is substantially different from what @Daniel Lichtblau proposed, but it directly uses your code up to the final Solve expression, where it also uses the trick of squaring in order t …

In Mathematica: Reduce[ForAll[{x, y}, x <= y \[Equivalent] x < y + 1], Integers] (* True *) or: Resolve[ForAll[{x, y}, x <= y \[Equivalent] x < y + 1], Integers] (* True *) For a mathem …