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  • ...can be drawn without taking the pencil off the paper. To rigorously define continuous functions, more complex mathematics is necessary. A function <math>f:E\to\mathbb{R}</math> is called ''continuous'' at some point in its domain <math> x_{0} </math> if, for all <math> \vare
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...me, dissimilar, completely different". In [[combinatorics]], two or more [[variable]]s are said to be discrete when they are independent or [[disjoint]]. *[[Continuous]]
    290 bytes (37 words) - 16:53, 8 September 2006
  • ...tarrow c} f(x) = f(c)</math>). This is because the function we chose was [[continuous]] at <math>c</math>. ...ose we want to be (for ''any'' <math>\epsilon > 0</math>), we can make our variable close enough (within a distance <math>\delta</math>, for some <math>\delta<
    7 KB (1,327 words) - 17:39, 28 September 2024
  • ...obability of that particular outcome. If the event <math>Z</math> has a [[continuous]] probability distribution, then <math>E(Z) = \int_z P(z)\cdot z\ dz</math> * For any random variable <math>X</math> and constant <math>c</math>, <cmath>\text{E}[X+c]=\text{E}[X
    5 KB (789 words) - 19:56, 10 May 2024
  • Let <math>ABCDA_1B_1C_1D_1</math> be a cube and <math>P</math> a variable point on the side <math>[AB]</math>. The perpendicular plane on <math>AB</m a) If the function is also continuous on <math>[0,1]</math> is it true that <math>f</math> is increasing?
    11 KB (1,779 words) - 13:57, 7 May 2012
  • ...nd is thus a [[continuous variable]] since its possible range of values is continuous.
    504 bytes (79 words) - 13:26, 8 December 2007
  • ...ressions, though Euler himself generalized the concept to what we now call continuous functions. This began a long debate over how "function" should be defined ...ynomial in <math>n+1</math> variables to be a polynomial in <math>1</math> variable over a polynomial ring in <math>n</math> variables), although here again so
    12 KB (2,010 words) - 23:10, 2 August 2020
  • ...pose there is a continuous function <math>f(x,y)</math> and there exists a continuous constraint function on the values of the function <math>c = g(x,y)</math>. ...>d = h(x, y, z)</math>, then we would add the partial with respect to each variable to their respective equation with another factor <math>\mu</math>. Thus, we
    5 KB (791 words) - 20:06, 30 November 2020
  • ...the first semester and a half of a typical year-long introductory, single-variable college calculus course, while AP Calculus BC is allegedly equal to the ful **Showing a function is continuous at a point
    5 KB (670 words) - 17:58, 21 February 2025
  • ...all) of the theorems typically presented to students in courses in single-variable calculus are proven rigorously; however, one should note that courses in re ...ities at points not in its domain (for example, <math>f(x) = 1/x</math> is continuous at all points in its domain yet is "visually discontinuous" at <math>x = 0<
    9 KB (1,409 words) - 01:41, 30 May 2023