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- A function <math>f:A\to B</math> is called [[monotonically increasing]] if <math>f(x_1)\geq f(x_2) </math> holds whenever <math>x_1>x_2 </math>. then the function is called [[strictly increasing]].10 KB (1,761 words) - 02:16, 12 May 2023
- ...(note that the sequence must be increasing on all terms, not monotonically increasing) <math>a_{10} < \frac{a_{10}^2}{a_{9}} \rightarrow a_{9} < a_{10}</math>3 KB (547 words) - 10:41, 7 August 2024
- ...decreasing on the [[interval]] <math>(-\infty, 0]</math> and monotonically increasing on the interval <math>[0, \infty)</math>. However, the function <math>f(x) More formally, a function <math>f</math> is monotonically increasing (resp. decreasing) if <math>a \leq b \Longrightarrow f(a) \leq f(b)</math>1 KB (155 words) - 16:15, 22 August 2006
- ...x_n)</math>, <math>P_n^{-1}(0)=0</math>, <math>P_n^{-1}</math> is strictly increasing in <math>[0,+\infty)</math>, and <math>\displaystyle \lim_{x_1 \rightarrow ...\forall m>n</cmath>and therefore the sequence <math>\{x_n\}</math> will be monotonically decreasing after one point.9 KB (1,784 words) - 16:40, 15 October 2024
- ...>x,y=x^x,z=x^{x^x}</math> with <math>.9<x<1.0</math>. Arranged in order of increasing magnitude, they are: ...h>. Because <math>0<x<1</math>, <math>f(n)=\log_x(n)</math> is [[monotonic|monotonically decreasing]], so the order of terms by magnitude in our new set of numbers2 KB (373 words) - 06:56, 18 July 2024
- ...that <math>A(x),B(x),C(x),D(x),</math> and <math>E(x)</math> are strictly increasing functions with range <math>(-\infty,\infty).</math> So, each polynomial has ...math>x</math>, and <math>A(x),B(x),C(x),D(x),</math> are all monotonically increasing functions, its real root must be the greatest, thus, the answer is <math>\b12 KB (2,016 words) - 05:58, 29 July 2024
- ...monotonically increasing subsequences (Case 1). Consider any monotonically increasing subsequence that starts at <math>x = a</math> and ends at <math>x = b</math9 KB (1,607 words) - 09:27, 4 February 2022
- ...cally increasing functions, so <math>x^3 + x - 8</math> is a monotonically increasing function. Thus, we can suspect that <math>(2,2,2)</math> is the only solut Assume that <math>x > 2</math>. Because <math>x^3</math> is a monotonically increasing function, <math>x^3 > 8</math>, so <math>x^3 - 8 > 0</math> and <math>x^3 +2 KB (340 words) - 00:16, 19 March 2020