FeiWuLiuZiao's blog

A math problem
By FeiWuLiuZiao, history, 3 hours ago, In English

There are some functions $$$T_y$$$, which are defined as:

  • $$$\forall j\le 1,y\in (0,1):T_y(j):=1$$$
  • $$$\forall y\in (0,1):T_y(x):=T_y(xy)+T_y(x-xy)+1$$$

Find $$$y$$$ (s) so that the order of $$$\lim_{x\rightarrow+\infty}T_y(x)$$$ is minimized.

  • Vote: I like it
  • +3
  • Vote: I do not like it

»
107 minutes ago, # |
  Vote: I like it 0 Vote: I do not like it

There is a bug in my latex , cannot figure it out , btw , if I'm not wrong, it's about caring only about second part since we're looking at limit of $$$\infty$$$ , by doing some equations , you should get $$$f_i(x)=-1$$$ for $$$1 < x < \infty$$$ that works ,and that's probably the minimum.

→ Reply
  • »
    »
    75 minutes ago, # ^ |
      Vote: I like it 0 Vote: I do not like it

    what are the equationgs

    does your $$$i$$$ mean the imaginary unit

    $$$x,y,j\in\mathbb{R}$$$ here

    → Reply
    • »
      »
      »
      68 minutes ago, # ^ |
        Vote: I like it 0 Vote: I do not like it

      I solved in integers , in this case my solution is almost wrong.

      → Reply