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A math problem
By FeiWuLiuZiao, history, 2 months 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.

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2 months ago, # |
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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.

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    2 months ago, # ^ |
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    what are the equationgs

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

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

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      2 months ago, # ^ |
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      I solved in integers , in this case my solution is almost wrong.

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2 months ago, # |
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in the second equation is it x>1 ? because in first equation it is defined for all j<=1. thank you.

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2 months ago, # |
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I guess that a solution is $$$y=\frac{1}{2}$$$

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