Search results

  • ===Monotonic functions=== ...inuity at <math> x_{0} </math> is equivalent with the following: for every sequence <math> (x_n)_{n\geq 0} </math> such that <math>\lim_{n\to\infty}x_n=x_0 </m
    10 KB (1,761 words) - 02:16, 12 May 2023
  • ...a_2, \ldots</math> approaches a [[limit]] of [[zero (constant) | zero]] [[monotonic]]ally then the series converges.
    2 KB (301 words) - 21:13, 19 February 2022
  • ...\infty)</math>. However, the function <math>f(x) = x^2</math> is ''not'' monotonic over the entire real line because it sometimes increases and sometimes decr ...(b)</math> (resp. <math>f(a) \geq f(b)</math>. The function is ''strictly monotonic'' if, in addition, <math>a \neq b \Longrightarrow f(a) \neq f(b)</math>.
    1 KB (155 words) - 16:15, 22 August 2006
  • ...\leq x_3 \leq \ldots</math>. If <math>x_1 < x_2 < x_3 \ldots</math>, the sequence is called ''strictly increasing''. * [[Decreasing sequence]]
    323 bytes (47 words) - 20:29, 24 October 2006
  • ...\geq x_3 \geq \ldots</math>. If <math>x_1 > x_2 > x_3 \ldots</math>, the sequence is called ''strictly decreasing''. * [[Increasing sequence]]
    322 bytes (47 words) - 20:30, 24 October 2006
  • ...e four digits in <math>2007</math>. A set of plates in which each possible sequence appears exactly once contains N license plates. Find N/10. ...{i+1}</math> if <math>a_{i}</math> is [[even]]. How many four-digit parity-monotonic integers are there?
    9 KB (1,435 words) - 00:45, 6 December 2021
  • Let <math>a_0<a_1<a_2<\cdots \quad </math> be an infinite sequence of positive integers, Prove that there exists a unique integer <math>n\ge1< Thus, <math>f(n) > f(n+1)</math>; i.e., <math>f</math> is monotonic decreasing. Therefore, because <math>f(0) > 0</math>, there exists a unique
    3 KB (611 words) - 10:16, 8 July 2023