Re: Analysis with tan x.

On May 4, 4:54 am, mina_wo...@xxxxxxxxxxx wrote:
Hello teacher~

tan_1 x = tan x
tan_2 x = tan(tan_1 x) = tan(tan x)
...
tan_k x = tan(tan_(k-1) x)

Find the lim{x -> 0} (tan_50 x) / x.

Answer : 1

0 is a fixed point of tan: R -> R
and d/dx tan (0) = 1

these properties do not change in iteration

(in general
if d/dx f (0) = a
then d/dx f(f(f(..(f(.))..) (0) = a^n
----n times------
)

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