Question

Помогите пожалуйста.​

Answer 1

$1); ; limlimits _{x to infty}frac{x^5+x^4+2x^2}{x^3-5x^5+x^4}=limlimits _{n to infty}frac{1+frac{1}{x}+frac{2}{x^3}}{frac{1}{x^2}-5+frac{1}{x}}=-frac{1}{5}\\2); ; limlimits _{x to 20}frac{sqrt{x+5}-5}{x-2x+20}=limlimits _{x to 20}frac{x+5-25}{(-x+20)(sqrt{x+5}+5)}=limlimits _{x to 20}frac{x-20}{-(x-20)(sqrt{x+5}+5)}=\\=limlimits _{x to 20}frac{1}{-(sqrt{x+5}+5)}=frac{1}{-sqrt{25}-5}=-frac{1}{10}$

$3); ; y=sin^32x+cos^25x\\y'=3cdot sin^22xcdot cos2xcdot 2+2cos5xcdot (-sin5x)cdot 5=\\=6cdot sin^22xcdot cos2x-5sin10x\\4); ; y=ln(x^2+5x+1)\\y'=frac{1}{x^2+5x+1}cdot(2x+5)\\5); ; y=(sinx)^{cos2x}\\lny=cos2xcdot ln(sinx)\\frac{y'}{y}=-2sin2xcdot ln(sinx)+cos2xcdot frac{cosx}{sinx}=-2sin2xcdot ln(sinx)+cos2xcdot tgx\\6); ; left { {{y=t^2+2t+1} atop {x=t+1}} right. ; ; ,; quad t=x-1\\y'_{x}=frac{y'_{t}}{x'_{t}}=frac{2t+2}{1}=2t+2=2(t+1)=2(x-1+1)=2x$