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A Estimation of a function

  1. Jul 3, 2016 #1
    Let ##x(t)\in C^1(\mathbb{R}_+,\mathbb{R}^m)## be a vector-function such that

    1) ##\|x(t)\|+\|\dot x(t)\|\to 0## as ##t\to\infty## and

    2) for all ##t>0## one has ##\|x(t)\|\le c_1\|\dot x(t)\|##


    Is it true that ##\|x(t)\|\le c_2 e^{-c_3t}##? Here ##c_i## are positive constants.
     
  2. jcsd
  3. Jul 3, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    No.$$x(t)= \frac{1}{t^3} \left(sin(t^2),cos(t^2)\right)$$
     
  4. Jul 3, 2016 #3
    shame on me. Thanks!
     
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