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  • Solutions can be written in [[interval notation]]. Closed bounds use square brackets, while open bounds (and bounds at inf For the sake of better notation, define the "x-intercept" of a fractional inequality to be those values of
    12 KB (1,806 words) - 05:07, 19 June 2024
  • * In any closed interval <math>[a, b]</math>, there exist real numbers <math>c</math> and <math>d</m ...vex'') in the interval <math>[a,b] </math> if <math>f''(x)>0</math> in the interval <math>[a,b] </math> and concave down (or ''concave'') if <math>f''(x)<0 </m
    10 KB (1,761 words) - 02:16, 12 May 2023
  • :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 The notation <math>\lim_{x\to c}f(x) = L</math> would only be justifiable if the limit <
    7 KB (1,327 words) - 17:39, 28 September 2024
  • We first simplify all the messy notation in the <math>S_n</math> term. Note that the problem asks us to find the sma ...dot2^{k}}</math>. However, we did not consider powers of two yet(since our interval was strictly between powers of 2), so we have to add <math>\sum_{k=1}^{n}{2
    10 KB (1,702 words) - 21:23, 25 July 2024
  • ...math> are relatively prime positive integers, find <math> m+n. </math> The notation <math> [z] </math> denotes the [[floor function|greatest integer]] that is ...c{1}{2} , \frac{1}{8}, \frac{1}{32}, \cdots</math>, and the <math>y</math> interval is given by <math>\frac{4}{5} , \frac{4}{125}, \frac{4}{3125}, \cdots</math
    2 KB (303 words) - 17:43, 16 October 2024
  • 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 ...ABCD </math> is 640. Find <math> \lfloor 1000 \cos A \rfloor. </math> (The notation <math> \lfloor x \rfloor </math> means the greatest integer that is less th
    6 KB (965 words) - 15:36, 8 September 2019
  • ...th> be <math>2^x5^y</math> such that <math>x, y</math> are integers on the interval <math>[0, 6]</math>. ...changing the general content of this solution, that would be great. If the notation is correct, then just delete this footnote)
    6 KB (1,071 words) - 21:25, 9 October 2021
  • ...ether, we have <math>x<-1</math> or <math>0 < x < 1</math>, or in interval notation, <math>(-\infty, -1) \cup(0, 1)</math>. The only answer in that range is <
    3 KB (558 words) - 12:36, 10 July 2019
  • ...arbitrary triangle <math>ABC</math> has isoperimetric quotient (using the notation <math>[ABC]</math> for area and <math>s = \frac{a + b + c}{2}</math>): ...- \frac{2}{1 + \sec A \cos (A - 2x)}</cmath> is increasing on the desired interval, because <math>\cos (A - 2x)</math> is increasing on <math>0 < x < \frac{A}
    2 KB (376 words) - 22:29, 18 May 2015
  • ...because <math>0 < x \le 1</math>, and <math>-x^2 - x + 3 > 0</math> on the interval <math>(0, 1]</math>. are less than the hypotenuse). Just for the sake of notation,
    10 KB (1,766 words) - 19:21, 10 November 2024
  • We claim that in the interval <math>(b^p, b^{p+1}]</math> there exists an unrepresentable number, for eve I hope this solution is quite intuitive, because it is without complicated notation. It didn't take me very long to discover.
    5 KB (1,009 words) - 02:09, 24 June 2024
  • Let b be a real number randomly selected from the interval <math>[-17,17]</math>. Then, m and n are two relatively prime positive inte ...st two distinct real solutions when <math>b</math> is randomly picked from interval <math>[-17,17]</math> is <math>\frac{29}{34}</math>. This means that <math
    2 KB (276 words) - 14:49, 20 June 2018
  • In interval notation, the solutions of the equation are <math>\boxed{(-\sqrt{1002}, -\sqrt{1001}
    2 KB (325 words) - 10:50, 17 March 2020
  • ...sum of this convergent series. Let <math>I\subset \mathbb{R}</math> be the interval <math>[-L,L]</math> (or any bounded subset of measure <math>\geq 2L</math>) Let <math>U_j</math> be the interval <math>(x_j-\frac{1}{|m-j|^a},x_j+\frac{1}{|m-j|^a})</math>, of length <math
    6 KB (1,068 words) - 02:20, 24 January 2024
  • ...e first couple "blocks" that Tadd has (a block will be denoted in interval notation): [<math>1</math>], [<math>7</math>-<math>10</math>], [<math>22</math>-<mat <math>1</math>) The start points of each interval is increasing arithmetically by <math>9</math>.
    6 KB (1,052 words) - 16:48, 6 November 2021
  • ...<math>7</math> inches more than during the previous <math>1</math>-second interval. The cart takes <math>30</math> seconds to reach the bottom of the hill. Ho where <math>a</math> and <math>b</math> are digits, he did not notice the notation and just multiplied <math>66</math> times <math>\underline{1}.\underline{a}
    15 KB (2,304 words) - 14:29, 14 October 2024
  • where <math>a</math> and <math>b</math> are digits, he did not notice the notation and just multiplied <math>66</math> times <math>\underline{1}.\underline{a} ...s x\right)=\cos \left( \frac{\pi}2 \sin x\right)</math> have in the closed interval <math>[0,\pi]</math>?
    15 KB (2,383 words) - 08:49, 25 June 2023
  • ...o\mathbb{R}</math>. Conventionally, sequences are typically denoted by the notation <math>(s_n)_{n = k}^{\infty} = (s_k,s_{k + 1},\ldots)</math> where <math>f( '''Definition''': Let <math>P</math> be a [[Partition of an interval|tagged partition]] of <math>[a,b]</math>. Then the Riemann sum correspondin
    9 KB (1,409 words) - 01:41, 30 May 2023
  • (The notation <math>\lfloor\cdot\rfloor</math> denotes the floor function; indices taken Continuing from Lemma 2's notation, if <math>B=\left\{b_0, b_1, \ldots, b_{m-1}\right\} \subseteq \Omega</math
    13 KB (2,406 words) - 04:36, 25 May 2024
  • (The notation <math>\lfloor\cdot\rfloor</math> denotes the floor function; indices taken Continuing from Lemma 2's notation, if <math>B=\left\{b_0, b_1, \ldots, b_{m-1}\right\} \subseteq \Omega</math
    13 KB (2,411 words) - 15:39, 4 June 2024

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