4) у=5/(√-х- √2
2)у(-х)=3(-х)³-4(-х)^5+1/(-x)²=-3x³+4x^5+1/x²≠-y(x)≠y(x)
четностью не обладает
10. Воспользуемся формулой производной частного.
![\displaystyle y'= \frac{(\arcsin 2x)'\cdot x^2-\arcsin2x\cdot (x^2)'}{x^4} =\\ \\ \\ = \frac{ \frac{1}{ \sqrt{1-4x^2} }\cdot(2x)'\cdot x^2-\arcsin2x\cdot 2x }{x^4} = \frac{2x-2 \arcsin2x\sqrt{1-4x^2} }{x^3 \sqrt{1-4x^2} }](https://tex.z-dn.net/?f=%5Cdisplaystyle+y%27%3D+%5Cfrac%7B%28%5Carcsin+2x%29%27%5Ccdot+x%5E2-%5Carcsin2x%5Ccdot+%28x%5E2%29%27%7D%7Bx%5E4%7D+%3D%5C%5C+%5C%5C+%5C%5C+%3D+%5Cfrac%7B+%5Cfrac%7B1%7D%7B+%5Csqrt%7B1-4x%5E2%7D+%7D%5Ccdot%282x%29%27%5Ccdot+x%5E2-%5Carcsin2x%5Ccdot+2x+%7D%7Bx%5E4%7D+%3D+%5Cfrac%7B2x-2+%5Carcsin2x%5Csqrt%7B1-4x%5E2%7D+%7D%7Bx%5E3+%5Csqrt%7B1-4x%5E2%7D+%7D+)
11. Здесь пользуемся формулой производной произведения.
![y'=(e^{-x}\sin 2x)'=(e^{-x})'\cdot \sin2x+e^{-x}\cdot (\sin 2x)'=\\ \\ =e^{-x}\cdot (-x)'\cdot \sin2x+e^{-x}\cdot \cos2x\cdot (2x)'=-e^{-x}(\sin 2x-2\cos 2x)](https://tex.z-dn.net/?f=y%27%3D%28e%5E%7B-x%7D%5Csin+2x%29%27%3D%28e%5E%7B-x%7D%29%27%5Ccdot+%5Csin2x%2Be%5E%7B-x%7D%5Ccdot+%28%5Csin+2x%29%27%3D%5C%5C+%5C%5C+%3De%5E%7B-x%7D%5Ccdot+%28-x%29%27%5Ccdot+%5Csin2x%2Be%5E%7B-x%7D%5Ccdot+%5Ccos2x%5Ccdot+%282x%29%27%3D-e%5E%7B-x%7D%28%5Csin+2x-2%5Ccos+2x%29)
Вторая производная:
![y''=(-e^{-x})'\cdot (\sin2x-2\cos2x)-e^{-x}\cdot(\sin2x-2\cos2x)'=\\ \\ =e^{-x}\cdot (\sin 2x-2\cos 2x)-e^{-x}\cdot (2\cos 2x+4\sin 2x)=\\ \\ \\ =e^{-x}\sin2x-2e^{-x}\cos2x-2e^{-x}\cos2x-4e^{-x}\sin2x=\\ \\ \\ =-3e^{-x}\sin2x-4e^{-x}\cos2x=-e^{-x}(3\sin2x+4\cos 2x)](https://tex.z-dn.net/?f=y%27%27%3D%28-e%5E%7B-x%7D%29%27%5Ccdot+%28%5Csin2x-2%5Ccos2x%29-e%5E%7B-x%7D%5Ccdot%28%5Csin2x-2%5Ccos2x%29%27%3D%5C%5C+%5C%5C+%3De%5E%7B-x%7D%5Ccdot+%28%5Csin+2x-2%5Ccos+2x%29-e%5E%7B-x%7D%5Ccdot+%282%5Ccos+2x%2B4%5Csin+2x%29%3D%5C%5C+%5C%5C+%5C%5C+%3De%5E%7B-x%7D%5Csin2x-2e%5E%7B-x%7D%5Ccos2x-2e%5E%7B-x%7D%5Ccos2x-4e%5E%7B-x%7D%5Csin2x%3D%5C%5C+%5C%5C+%5C%5C+%3D-3e%5E%7B-x%7D%5Csin2x-4e%5E%7B-x%7D%5Ccos2x%3D-e%5E%7B-x%7D%283%5Csin2x%2B4%5Ccos+2x%29)
12. Наклонная асимптота является линейной функцией. В общем виде можно представить как y = kx + b
По определению асимптоты:
![\displaystyle \lim_{x \to \infty} (kx+b-f(x))](https://tex.z-dn.net/?f=%5Cdisplaystyle++%5Clim_%7Bx+%5Cto+%5Cinfty%7D+%28kx%2Bb-f%28x%29%29)
![k=\displaystyle \lim_{x \to \infty} \frac{f(x)}{x}= \lim_{x \to \infty} \frac{3x^2+5x+1}{x(2x+1)} = \frac{3}{2}](https://tex.z-dn.net/?f=k%3D%5Cdisplaystyle++%5Clim_%7Bx+%5Cto+%5Cinfty%7D+%5Cfrac%7Bf%28x%29%7D%7Bx%7D%3D++%5Clim_%7Bx+%5Cto+%5Cinfty%7D+%5Cfrac%7B3x%5E2%2B5x%2B1%7D%7Bx%282x%2B1%29%7D+%3D+%5Cfrac%7B3%7D%7B2%7D+)
Найдем теперь коэффициент b
![\displaystyle b= \lim_{x \to \infty}(f(x)-kx)= \lim_{x \to \infty} \bigg(\frac{3x^2+5x+1}{2x+1}- \frac{3x}{2} \bigg)=\\ \\ \\ = \lim_{x \to \infty} \frac{7x+2}{4x+2} = \frac{7}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle+b%3D+%5Clim_%7Bx+%5Cto+%5Cinfty%7D%28f%28x%29-kx%29%3D+%5Clim_%7Bx+%5Cto+%5Cinfty%7D+%5Cbigg%28%5Cfrac%7B3x%5E2%2B5x%2B1%7D%7B2x%2B1%7D-+%5Cfrac%7B3x%7D%7B2%7D+%5Cbigg%29%3D%5C%5C+%5C%5C+%5C%5C+%3D+%5Clim_%7Bx+%5Cto+%5Cinfty%7D+%5Cfrac%7B7x%2B2%7D%7B4x%2B2%7D+%3D+%5Cfrac%7B7%7D%7B4%7D+)
Получим уравнение наклонной асимптоты:
![y= \dfrac{3x}{2} + \dfrac{7}{4}](https://tex.z-dn.net/?f=y%3D+%5Cdfrac%7B3x%7D%7B2%7D+%2B+%5Cdfrac%7B7%7D%7B4%7D+)
Фото:::::::::::::::::::::::::::::::
Точно не знаю. 4 умножить на 12 км, и 5 на 12 =1) 48 2) 50