Question

varianta 1 va rog urgent

Answer 1

se da legea de compozitie x*y=x+y-2016
a)2016*2=2016+2-21016=2
b)x*x=1⇒x+x-2016=1⇒2x-2016=1⇒2x=2016+1⇒2x=2017⇒x=2017/2⇒x=1008.5
c)elementul neutru
x*e=e*x=x
x*e=x+e-2016=x⇒x+e-2016-x=0⇒e-2016=0⇒e=2016,e∈R

d)x*x²=-2016⇒x+x²-2016=-2016⇒x²+x-2016+2016=0⇒x²+x+0=0

a=1
b=1
c=0
Δ=b²-4ac⇒Δ=1²-4×1×0⇒Δ=1+0⇒√Δ=√1⇒Δ=1
x1x2=-b+-√Δ/2a⇒
x1=-1+1/2⇒x1=0
x2=-1-1/2⇒x2=-2/2⇒x2=-1

2)se da functia inR,f(x)=x²
a)F(x)=1/3
x³+2016 este o primitiva a functiei f(x) 
1/2×x³
se foloseste formula 
f/g si f*g
(f/g)*=f*×g-f×g*/g²
(f×g)*=f*×g+f×g*
si prin calcule rezulta urmatoarele:
(1/2*x³)*=(1/3)*×x³+[1/2×(x³)*]=
0×x³+[1/3×3x²]=0+x²=x²
(2016)*=0
stim ca orice nr constant derivat rezultatul este 0
F(X)*=X²+0⇒F(X)*=X².⇒F(x)=este o primitiva a functiei f(x)=
b)∫₀¹f(x)dx=∫₀¹x²dx=x³/3/₀¹=1³/3-0³/3=1/3

c)V=g(x)
g(x)=f(x)
V=π∫g(x)²⇒V=π∫f(x)²⇒π∫₀¹(x²)²dx=π∫₀¹x⁴dx⇒π(x⁵/5)/₀¹⇒π(1⁵/5-0⁵/5)⇒π1/5
mult sucees  si bafta la bac