Если y=e^(-x²), то y'=-2*x*e^(-x²)
Если y(-x) = y(x) -- функция четная,
если y(-x) = -y(x) -- функция нечетная.
![1) \: \: y( - x) = 3cos( - x)sin( - x) - tg( - x) = 3cosx \times ( - sinx) - ( - tgx) = - 3cosxsinx + tgx = - (3cosxsinx - tgx) = - y(x)](https://tex.z-dn.net/?f=1%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+3cos%28+-+x%29sin%28+-+x%29+-+tg%28+-+x%29+%3D+3cosx+%5Ctimes+%28+-+sinx%29+-+%28+-+tgx%29+%3D+-+3cosxsinx+%2B+tgx+%3D+-+%283cosxsinx+-+tgx%29+%3D+-+y%28x%29)
=> функция нечетная.
![2) \: \: y( - x) = {tg}^{2} ( - x) - 5cos( -x) \div sin( - x) = {tg}^{2} x - 5cosx \div ( - sinx) = {tg}^{2} x + 5cosx \div sinx](https://tex.z-dn.net/?f=2%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+%7Btg%7D%5E%7B2%7D+%28+-+x%29+-+5cos%28+-x%29+%5Cdiv+sin%28+-+x%29+%3D+%7Btg%7D%5E%7B2%7D+x+-+5cosx+%5Cdiv+%28+-+sinx%29+%3D+%7Btg%7D%5E%7B2%7D+x+%2B+5cosx+%5Cdiv+sinx)
=> функция ни четная, ни нечетная.
![3) \: \: y( - x) = - x \times ctg( - x) - 2cos( - x) = - x \times ( - ctgx) - 2cosx = xctgx - 2cosx = y(x)](https://tex.z-dn.net/?f=3%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+-+x+%5Ctimes+ctg%28+-+x%29+-+2cos%28+-+x%29+%3D+-+x+%5Ctimes+%28+-+ctgx%29+-+2cosx+%3D+xctgx+-+2cosx+%3D+y%28x%29)
=> функция четная.
![4) \: \: y( - x) = {sin}^{2}(-x) - cos(-x) + {(-x)}^{3} tg(-x) = {sin}^{2}x - cosx - ({x}^{3}) \times (-tgx) = {sin}^{2} - cosx + {x}^{3}tgx = y(x)](https://tex.z-dn.net/?f=+4%29+%5C%3A+%5C%3A+y%28+-+x%29+%3D+%7Bsin%7D%5E%7B2%7D%28-x%29+-+cos%28-x%29+%2B+%7B%28-x%29%7D%5E%7B3%7D+tg%28-x%29+%3D++%7Bsin%7D%5E%7B2%7Dx+-+cosx+-+%28%7Bx%7D%5E%7B3%7D%29+%5Ctimes+%28-tgx%29+%3D+%7Bsin%7D%5E%7B2%7D+-+cosx+%2B+%7Bx%7D%5E%7B3%7Dtgx+%3D+y%28x%29+)
=> функция четная.
![5) \: \: y( -x) = 2sin(-x) - cos(-x) = -2sinx - cosx](https://tex.z-dn.net/?f=+5%29+%5C%3A+%5C%3A+y%28+-x%29+%3D+2sin%28-x%29+-+cos%28-x%29+%3D+-2sinx+-+cosx+)
=> функция ни четная, ни нечетная.
Tc(5π/2-x)=ctgx=-√2
sin²x=1:(1+ctg²x)=1:(1+2)=1/3
sinx=1/√3
cosx=-√(1-sin²x)=-√(1-1/3)=-√6/3
cos(π/4+x)=cosπ/4cosx-sinπ/4sinx=
=√2/2*(-√6/3)-√2/2*√3/3=√2/2(-√6/3-√3/3)=-√6/6*(√2+1)
3x -10x >= 5+2
-7х>=7
х<=1