mathematics

1.f is a function defined on r, m = {x | f (x) = x}, n = {x | f (f (x)) = x}.

(1) verification: m belongs to n.

(2) If f monotonically increases on r, is there M=N? And explain why. This way is ok, use the counter-evidence.

2. Given that SIN (x+20) = COS (x+10)+COS (x-10), find tanx.

3. Parabolic equation y=sqr(x), make n regular triangles, and find the side length of the nth triangle.

Party A and Party B toss a coin with even texture, and the head that is thrown first wins. Throw a failed game first and ask:

(1) The probability that the first thrower wins. Take the limit.

(2) If A throws first in the first game, what is the probability of A winning in the N game?

I forgot specifically. Anyway, I used Cauchy inequality.

I'm not very good at pictures. ...