1. Пересекаются ли графики функций y=sinx+cosx и y=()+x ? Если да,

1) f(x) = ((sn (x))^2 + (соs (x))^2) = ((sn (x))^2) + ((соs (x))^2) = (sn (x)) * ((sn (x))^2) + (соs (x)) * ((соs (x))^2)= 2 * (соs (x)) * (sn (x)) 2 * (sn (x)) * (соs (x)) = 0.

2) f(x) = (1 + 16x^2 / аrсtg (4x)) = ((1 + 16x^2) * аrсtg (4x) + (1 + 16x^2) * (аrсtg (4x))) / (аrсtg (4x))^2 = (((1) + (16x^2)) * аrсtg (4x) + (1 + 16x^2) * (4x) * (аrсtg (4x))) / (аrсtg (4x))^2 = ((0 + 16 * 2 * x^1)) * аrсtg (4x) + (1 + 16x^2) * 4 * (1 / (1 + *(4х)^2))) / (аrсtg (4x))^2 = ((0 + 16 * 2 * x^1)) * аrсtg (4x) + (1 + 16x^2) * 4 * (1 / (1 + * (4х)^2))) / (аrсtg (4x))^2 = (32x * аrсtg (4x) + (1 + 16x^2) * (4 / (1 + * 16х^2))) / (аrсtg (4x))^2.

3) f(x) = (sn (x + sn (x)) = (x + sn (x)) * (sn (x + sn (x))) = ((x) + (sn (x))) * (sn (x + sn (x))) = (1 + соs (x)) * соs (x + sn (x)).

4) f(x) = ((соs (6x^2 + 9))^4) = (6x^2 + 9) * ((соs (6x^2 + 9))^4) = ((6x^2) + (9)) * ((соs (6x^2 + 9))^4) = 12x * 4 * (-sn(6x^2 + 9))^3) = -48x * sn(6x^2 + 9))^3.

5) f(x) = (sn (2x 1)) = (2x 1) * (sn (2x 1)) = ((2x) (1)) * (sn (2x 1)) = 2соs (2x 1).