F(x) = x² + 3x - 1
f '(x) = (x²)' + 3(x)' - 1' = 2x + 3
f(x) = x³(4 + 2x - x²) = 4x³ + 2x⁴ - x⁵
f '(x) = 4(x³)' + 2(x⁴)' - (x⁵)' = 12x² + 8x³ - 5x⁴
f(x) = x²(3x + x³) = 3x⁴ + x⁵
f '(x) = 3(x⁴)' + (x⁵)' = 12x³ + 5x⁴
f(x) = x² - 3x
f '(x) = (x²)' - 3(x)' = 2x - 3
f '(1/2) = 2 * 1/2 - 3 = - 2
f '(2) = 2 * 2 - 3 = 1
Под буквой А правильный ответ.
2)log12(27)=a;log6(16)=?
log12(3^3)=3•log3(3)/log3(12)=3/(log3(3)+2log3(2))=3/(1+2log3(2))=a
3=a+2alog3(2)
log3(2)=(3-a)/2a
log6(16)=4log6(2)=4•log3(2)/log3(6)=
4log3(2)/(1+log3(2))=4(3-a)/2a:(1+(3-a)/2a)=
2(3-a)/a:(a+3)/2a=2(3-a)/a*2a/a+3=
4(3-a)/(3+a)
3)a)log30(x)=1/logx(30)=
1/(logx(5)+logx(2)+logx(3))
b)1/(log2(x)•log3(x)•log5(x))
*1/(logx(5)+logx(2)+logx(3))=
log2(x)•log3(x)+log3(x)•
log5(x)+log5(x)•log2(x)
c)(log2(x)•log3(x)+log3(x)•
log5(x)+log5(x)•log2(x)):
(log2(x)•log3(x)+log3(x)•
log5(x)+log5(x)•log2(x))
=1
1 вар:
1) а) кор(9)*кор(0,64)=3*0,8=2,4;
б)кор(36/25*64/25)=6/5*8/5=48/25=1,92;
в)кор(1764)=42;
г)кор(3,2*80)=кор(256)=16
д)кор(162/2)=кор(81)=9;
2)кор((26-24)*(26+24))=кор(2*50)=кор(100)=10;
2 вар:
1) а)6*1,1=6,6;
б)кор(81/25*100/49)=9/5*10/7=9*10/5*7=18/7;
в)кор(900)=30;
г)кор(2,7*120)=кор(324)=18;
д)кор(1/100)=1/10=0,1;
2)кор((29-21)*(29+21))=кор(8*50)=коо(400)=20;
вар 3:
1) а)7*1,5=10,5;
б)кор(121/49*25/4)=11/7*5/2=55/14;
в)кор(7056)=84;
г)кор(12,5*0,5)=кор(6,25)=2,5;
д)кор(50/1250)=кор(1/25)=1/5=0,2;
2)кор((28-22)*(28+22)/3)=кор(6*50/3)=кор(100)=10;