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  • ...is often left out of the ordinary educational track, they are common in [[mathematics Olympiads]]. Solutions can be written in [[interval notation]]. Closed bounds use square brackets, while open bounds (and boun
    12 KB (1,806 words) - 05:07, 19 June 2024
  • The trivial inequality is one of the most commonly used theorems in mathematics. It is very well-known and does not require proof. ...>a,b</math> and <math>c</math> are side lengths of a triangle, lies in the interval <math>(p,q]</math>, where <math>p</math> and <math>q</math> are rational nu
    3 KB (583 words) - 20:20, 2 August 2024
  • ...cil off the paper. To rigorously define continuous functions, more complex mathematics is necessary. * In any closed interval <math>[a, b]</math>, there exist real numbers <math>c</math> and <math>d</m
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...92653. The number pi is one of the most important [[constant]]s in all of mathematics and appears in some of the most surprising places, such as in the sum <math ...= 0</math>, which is considered to be one of the most beautiful results in mathematics since it involves five of the greatest [[constant]]s: [[e]], pi, [[i]], [[u
    8 KB (1,469 words) - 20:11, 16 September 2022
  • ...e more general settings of [[topology]], [[analysis]], and other fields of mathematics. It took several centuries to articulate the definition of a limit and to m :Let <math>f</math> be a function whose [[domain]] is a sub-interval of the real numbers and whose [[codomain]] is the set of reals. For a real
    7 KB (1,327 words) - 17:39, 28 September 2024
  • Let <math>x</math> be chosen at random from the interval <math>(0,1)</math>. What is the probability that * [[Mathematics competition resources]]
    13 KB (2,058 words) - 11:36, 4 July 2023
  • ...uld be a graph of <math>y = P(x)</math> and <math>y = Q(x)</math> over the interval <math>-4\leq x \leq 4</math>? * [[Mathematics competition resources]]
    12 KB (1,792 words) - 12:06, 19 February 2020
  • ...gle <math>\alpha</math>, measured in radians and chosen at random from the interval <math>(0,\pi)</math>, and moves <math>5</math> cm in a straight line to <ma ...<math>x</math>-intercepts on the graph of <math>y=\sin(1/x)</math> in the interval <math>(0.0001,0.001)</math> is closest to
    13 KB (1,987 words) - 17:53, 10 December 2022
  • ...e [[minimum]] value taken by <math>f(x)</math> for <math>x</math> in the [[interval]] <math>p \leq x\leq15</math>. * [[American Invitational Mathematics Examination]]
    7 KB (1,104 words) - 02:13, 27 May 2024
  • Mary told John her score on the American High School Mathematics Examination (AHSME), which was over <math>80</math>. From this, John was ab ...h>, what is the least number of roots <math>f(x)=0</math> must have in the interval <math>-1000\leq x \leq 1000</math>?
    6 KB (933 words) - 00:15, 19 June 2022
  • An angle <math> x </math> is chosen at random from the interval <math> 0^\circ < x < 90^\circ. </math> Let <math> p </math> be the probabil * [[American Invitational Mathematics Examination]]
    6 KB (965 words) - 15:36, 8 September 2019
  • Mary told John her score on the American High School Mathematics Examination (AHSME), which was over <math>80</math>. From this, John was ab ...\geq80}</math> and <math>\boldsymbol{s}</math> is contained in exactly one interval.</b></i>
    7 KB (1,181 words) - 00:53, 21 November 2024
  • If all <math>3</math> <math>n</math>s are in the same interval, there are <math>6</math> ways. If <math>2</math> of the <math>3</math> <math>n</math>s are in the same interval, there are <math>6\cdot5=30</math> ways.
    7 KB (1,115 words) - 23:52, 6 September 2023
  • ...ause a parabola contains two roots for each value of <math> y, </math> the interval length is 1. ...|x|<4. </math> The length of this interval is 8 and thus 40% of the given interval.
    9 KB (1,364 words) - 14:59, 21 July 2006
  • ...number of solutions to the equation <math>\sin{x}=\sin{(nx)}</math> on the interval <math>[0,\pi]</math>. What is <math>\sum_{n=2}^{2007} F(n)</math>? * [[Mathematics competition resources]]
    11 KB (1,750 words) - 12:35, 15 April 2022
  • ...hen red for <math>30</math> seconds. Leah picks a random three-second time interval to watch the light. What is the probability that the color changes while sh * [[Mathematics competition resources]]
    12 KB (1,814 words) - 11:58, 19 February 2020
  • How many zeros does <math>f(x) = \cos(\log x)</math> have on the interval <math>0 < x < 1</math>? * [[Mathematics competition resources]]
    13 KB (1,945 words) - 20:04, 2 February 2025
  • It can also be written as an interval in the following units: ! colspan="5" |[[Interval]]
    1 KB (157 words) - 17:38, 28 September 2024
  • ...ath>f:[a,b]\rightarrow\mathbb R</math> be differentiable function on the [[interval]] <math>(a,b)</math>. The '''Mean Value Theorem''' states there exists a po [[category:Mathematics]]
    1 KB (251 words) - 17:04, 28 September 2024
  • ...more than the product of its reciprocal and its additive inverse. In which interval does the number lie? * [[Mathematics competition resources]]
    14 KB (1,983 words) - 15:25, 2 June 2022

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