1)х^3+3х^2-4=(x-1)(x+2)^2
2)<span>х^3+9х^2+11х-21</span>=(x-1)(x+3)(x+7)
![(\frac{1}{3})^{5x^2+8x-4}<1](https://tex.z-dn.net/?f=+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B5x%5E2%2B8x-4%7D%3C1++)
![(\frac{1}{3})^{5x^2+8x-4}<(\frac{1}{3})^0](https://tex.z-dn.net/?f=+%28%5Cfrac%7B1%7D%7B3%7D%29%5E%7B5x%5E2%2B8x-4%7D%3C%28%5Cfrac%7B1%7D%7B3%7D%29%5E0++)
![5x^2+8x-4>0](https://tex.z-dn.net/?f=+5x%5E2%2B8x-4%3E0++)
![5x^2+8x-4=0](https://tex.z-dn.net/?f=+5x%5E2%2B8x-4%3D0++)
![D=8^2-4*5*(-4)=64+80=144](https://tex.z-dn.net/?f=+D%3D8%5E2-4%2A5%2A%28-4%29%3D64%2B80%3D144+)
![x_1=\frac{-8+12}{10}=0.4](https://tex.z-dn.net/?f=+x_1%3D%5Cfrac%7B-8%2B12%7D%7B10%7D%3D0.4++)
![x_2=\frac{-8-12}{10}=-2](https://tex.z-dn.net/?f=+x_2%3D%5Cfrac%7B-8-12%7D%7B10%7D%3D-2+)
![5(x-0.4)(x+2)>0](https://tex.z-dn.net/?f=+5%28x-0.4%29%28x%2B2%29%3E0+)
-/////////////-(-2)-------- - -------(0.4)-/////////////-
Ответ:
∞
∪
∞ ![)](https://tex.z-dn.net/?f=+%29+)
Фотка ниже я исправила( жаль что поздно так , предупреждение вывесили
Sin 390°=sin(360°+30°)=sin 30°=1/2
Уравнение касательной:
![y_{k}=y'(x)+y'(x_{0})(x-x_{0})](https://tex.z-dn.net/?f=y_%7Bk%7D%3Dy%27%28x%29%2By%27%28x_%7B0%7D%29%28x-x_%7B0%7D%29)
![y=cos(5x+ \frac{ \pi }{4})-4 \\ y'(x)=-sin(5x+ \frac{ \pi }{4})*(5x+ \frac{ \pi }{4})'=-5sin(5x+ \frac{ \pi }{4}) \\y'(x_{0})=-5sin\frac{ \pi }{4}=-5* \frac{ \sqrt{2}}{2}= \frac{-5 \sqrt{2}}{2}=-2,5 \sqrt{2} \\ \\ y_{k}=-5sin(5x+ \frac{ \pi }{4})-2,5 \sqrt{2}(x-0) \\ y_{k}=-5sin(5x+ \frac{ \pi }{4})-2,5 \sqrt{2}x](https://tex.z-dn.net/?f=y%3Dcos%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29-4+%5C%5C+y%27%28x%29%3D-sin%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29%2A%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29%27%3D-5sin%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29+%5C%5Cy%27%28x_%7B0%7D%29%3D-5sin%5Cfrac%7B+%5Cpi+%7D%7B4%7D%3D-5%2A+%5Cfrac%7B+%5Csqrt%7B2%7D%7D%7B2%7D%3D+%5Cfrac%7B-5+%5Csqrt%7B2%7D%7D%7B2%7D%3D-2%2C5+%5Csqrt%7B2%7D+%5C%5C++%5C%5C+y_%7Bk%7D%3D-5sin%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29-2%2C5+%5Csqrt%7B2%7D%28x-0%29+%5C%5C+y_%7Bk%7D%3D-5sin%285x%2B+%5Cfrac%7B+%5Cpi+%7D%7B4%7D%29-2%2C5+%5Csqrt%7B2%7Dx)
Ответ: у(k)=-5sin(5x+п/4)-2,5√2x это и есть уравнение касательной.