Задание В3
1 способ:
![y=\frac{\sin x}{\cos x}=tg x \\ \\ y'=(\frac{\sin x}{\cos x})'=(tgx)'=\frac{1}{\cos^2 x}\\ \\ y'(0)=\frac{1}{\cos^2 0}=\frac{1}{1^2}=1 y=\frac{\sin x}{\cos x}=tg x \\ \\ y'=(\frac{\sin x}{\cos x})'=(tgx)'=\frac{1}{\cos^2 x}\\ \\ y'(0)=\frac{1}{\cos^2 0}=\frac{1}{1^2}=1](https://tex.z-dn.net/?f=+y%3D%5Cfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D%3Dtg+x+%5C%5C+%5C%5C+y%27%3D%28%5Cfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D%29%27%3D%28tgx%29%27%3D%5Cfrac%7B1%7D%7B%5Ccos%5E2+x%7D%5C%5C+%5C%5C+y%27%280%29%3D%5Cfrac%7B1%7D%7B%5Ccos%5E2+0%7D%3D%5Cfrac%7B1%7D%7B1%5E2%7D%3D1+++++)
2 способ:
![y=\frac{\sin x}{\cos x} \\ \\ y'=(\frac{\sin x}{\cos x})'=\frac{(\sin x)'\cdot\cos x- \sin x\cdot(\cos x)'}{(\cos x)^2} =\frac{\cos x\cdot \cos x-\sin x\cdot(-\sin x)}{\cos^2 x} =\\\\=\frac{\cos^2 x+\sin^2 x}{\cos^2 x}=\frac{1}{\cos^2 x}\\ \\ y'(0)=\frac{1}{\cos^2 0}=\frac{1}{1^2}=1 y=\frac{\sin x}{\cos x} \\ \\ y'=(\frac{\sin x}{\cos x})'=\frac{(\sin x)'\cdot\cos x- \sin x\cdot(\cos x)'}{(\cos x)^2} =\frac{\cos x\cdot \cos x-\sin x\cdot(-\sin x)}{\cos^2 x} =\\\\=\frac{\cos^2 x+\sin^2 x}{\cos^2 x}=\frac{1}{\cos^2 x}\\ \\ y'(0)=\frac{1}{\cos^2 0}=\frac{1}{1^2}=1](https://tex.z-dn.net/?f=+y%3D%5Cfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D+%5C%5C+%5C%5C+y%27%3D%28%5Cfrac%7B%5Csin+x%7D%7B%5Ccos+x%7D%29%27%3D%5Cfrac%7B%28%5Csin+x%29%27%5Ccdot%5Ccos+x-+%5Csin+x%5Ccdot%28%5Ccos+x%29%27%7D%7B%28%5Ccos+x%29%5E2%7D+%3D%5Cfrac%7B%5Ccos+x%5Ccdot+%5Ccos+x-%5Csin+x%5Ccdot%28-%5Csin+x%29%7D%7B%5Ccos%5E2+x%7D+%3D%5C%5C%5C%5C%3D%5Cfrac%7B%5Ccos%5E2+x%2B%5Csin%5E2+x%7D%7B%5Ccos%5E2+x%7D%3D%5Cfrac%7B1%7D%7B%5Ccos%5E2+x%7D%5C%5C+%5C%5C+y%27%280%29%3D%5Cfrac%7B1%7D%7B%5Ccos%5E2+0%7D%3D%5Cfrac%7B1%7D%7B1%5E2%7D%3D1+++++)
Ответ: 1
Задание В4
0" alt=" (x-4)(x+1)=66\\ \\ x^2-4x+x-4-66=0\\ \\ x^2-3x-70=0 \\ \\ D=(-3)^2-4\cdot1\cdot(-70)=9+280=289>0" align="absmiddle" class="latex-formula">
Значит, уравнение имеет два корня
Пусть
и
-корни квадратного уравнения, тогда по теореме Виета ![\left \{ {{x_1+x_2=3} \atop {x_1\cdot x_2=-70}} \right. \left \{ {{x_1+x_2=3} \atop {x_1\cdot x_2=-70}} \right.](https://tex.z-dn.net/?f=+%5Cleft+%5C%7B+%7B%7Bx_1%2Bx_2%3D3%7D+%5Catop+%7Bx_1%5Ccdot+x_2%3D-70%7D%7D+%5Cright.++)
Сумма корней равна 3
Ответ: 3