1)сtg²a*sin²a=cos²a/sin²a*sin²a=cos²a
2)E(f)=-1/2*[-1;1]=[-1/2;1/2]
3)f`(x)=14x^6-4sinx
f`(0)=0
4)cosx(cosx-2)=0
cosx=0⇒x=π/2+πn
cosx=2>1 нет решения
5)1/(x+3) -1>0
(1-x-3)/(x+3)>0
(x+2)(x+3)<0<br>x=-2 x=-3
x∈(-3;-2)
6)1/2*(-π/3)+1/2*5π/6)=-π/6+5π/12=3π/12=π/4
7)y`=-2x+12x³
y`(-1)=2-12=-10
8)sinx<0<br>x∈(2πn;π+2πn)
9)x²/(1-x)(1+x)≥0
x=0 x=-1 x=1
+ _ _ +
------------------------------------------------------------------------------
-1 0 1
x∈(-∞;-1) U (1;∞)
B1)v(t)=10t+3=33
10t=33-3=30
t=30:10=3
B2)2cos4xcosx+cos2x=0
cos2x(2cos4x+1)=0
cos2x=0⇒2x=π/2+πn⇒x=π/4+πn/2
cos4x=-1/2⇒4x=+-2π/3+2πn⇒x=+-π/6+πn/2
B3)f`(x)=x²-x-6=0
x1+x2=1 U x1*x2=-6
x1=-2 U x2=3
+ _ +
--------------------------------------------------------------
-2 3
min
F(3)=9-4,5-18+25,5=12
B4)(1-x²)≥0⇒-1≤x≤1
x²-1≥0⇒x≤-1 U x≥1
Ответ x=-1;x=1
B5)f`(x0)=10
f`(x)=2ax+4
f`(-1)=-2a+4=10
-2ax=10-4=6
a=6:(-2)=-3