F(x)=4x²+9x⁻³
f`(x)=4*2*x+(-3)*9*x⁻⁴=8x-27x⁻⁴.
₁∫²(3x⁴+2x²-5)dx=(3x⁵/5+2x³/3-5x) ₁|²=3*2⁵/5+2*2³/3-5*2-3*1⁵/5-2*1³/3+5*1=
=96/5+16/3-10-3/5-2/3+5=93/5+14/3-5=(93*3+14*5)/15=
=349/15-5=23⁴/₁₅-5=18⁴/₁₅.
243 : 121,5 = 2 и 128 : 64 = 2
Или 243 : 243 = 1 и 128 : 128 = 1
Графики на фотографиях. всего хорошего)
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