E mult cea ce ceri.Iti voi rezolva pe S3
1.a) f `(x)=3x²-3/x=3(x³-1)/x
Aplici formula
A³-B³=(A-b)(A²+A*B+B²)
f `(x)=3(x-1)*(x²+x+1)/x
b)Asimptota vericala vei avea la dreapta lui 0.
x→0 ,x>0 lim f(x)=0³-3ln0=0-∞=-∞
x=0 asimptota verticala- axa Oy
c)f `(x)=0 =>x-1=0 x=1,
Pt x∈(0,1) f `(x)<0 .pt x≥1 f `(x)≥0 => x=1 punct de minim=>∀x>0, f(x)≥f(1)=1-3ln1=1-0=1
2a)
(x²+3x+3)*f(x)=2x+3
∫(2x+3)dx = x∈[1,2]
=∫2xdx+∫3dx=2x²/2+3x=(x²+3x)/1↑2=4+6-1-3=6
2b) Aria =integrala de la 0 la 3 din f(x)=
∫(2x+3)dx/(x²+3x+3) x∈[0,3]
notezi x²+3x+3=y obsrvi ca (x²+3x+3) `=2x+3
A=∫y `dy/y=lny=ln(x²+3x+3) /o↑3= ln 21-ln3=ln21/3=ln7
