Tg(a + π/4) = (tga + 1) / (1 - tga) = 0.2
0.2*(1 - tga) = tga + 1
0.2 - 0.2tga = tga + 1
-0.8 = 1.2tga
tga = -0.8/1.2
ctga = 1/tga = -1.2/0.8 = 1.5
2,25=1,5^2
2,25-у^2=2
переносим 2,25 за знак "равно" с противоположным знаком:
-у^2=2-2,25
-у^2=-0,25
у^2=0,25
у=±0,5
именно ±, потому что в квадрат можно возвести как положительное число, так и отрицательное и в квадрате оно будет положительным
Производную ищем, как производную произведения.
![f'(x)=( (x-1)* \sqrt{x+1} )'=( (x-1)* (x+1)^{ \frac{1}{2} } )'= \\ =(x-1)' *(x+1)^{ \frac{1}{2} } +(x-1)*((x+1)^{ \frac{1}{2} } )'= \\ =1*(x+1)^{ \frac{1}{2} } +(x-1)*\frac{1}{2}*(x+1)^{ -\frac{1}{2} } = \\ =(x+1)^{ \frac{1}{2} } +\frac{1}{2} *(x-1)* \frac{1}{(x+1)^{ \frac{1}{2} }} = \sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}}](https://tex.z-dn.net/?f=f%27%28x%29%3D%28+%28x-1%29%2A+%5Csqrt%7Bx%2B1%7D++%29%27%3D%28+%28x-1%29%2A+%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D+%5C%5C+%3D%28x-1%29%27+%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%28%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%29%27%3D++%5C%5C+%3D1%2A%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%28x-1%29%2A%5Cfrac%7B1%7D%7B2%7D%2A%28x%2B1%29%5E%7B+-%5Cfrac%7B1%7D%7B2%7D+%7D+%3D++%5C%5C+%3D%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D+%2B%5Cfrac%7B1%7D%7B2%7D+%2A%28x-1%29%2A+%5Cfrac%7B1%7D%7B%28x%2B1%29%5E%7B+%5Cfrac%7B1%7D%7B2%7D+%7D%7D+%3D+%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+)
Подставляем x = 3
![\sqrt{x+1} + \frac{x-1 }{ 2\sqrt{x+1}} = \sqrt{3+1} + \frac{3-1}{2 \sqrt{3+1} } =2+ \frac{1}{2} =2,5](https://tex.z-dn.net/?f=%5Csqrt%7Bx%2B1%7D+%2B+%5Cfrac%7Bx-1+%7D%7B+2%5Csqrt%7Bx%2B1%7D%7D+%3D+%5Csqrt%7B3%2B1%7D+%2B+%5Cfrac%7B3-1%7D%7B2+%5Csqrt%7B3%2B1%7D+%7D+%3D2%2B+%5Cfrac%7B1%7D%7B2%7D+%3D2%2C5)