1)tg(arctg3/4+arctg1/7)=tgπ/4
tg(arctg3/4+arctg1/7)=1
tg(arctg3/4+arctg1/7)=(tg(arctg3/4)+tg(arctg1/7))/(1-tg(arctg3/4)*tg(arctg1/7))=
=(3/4+1/7)/(1-3/4*1/7)=25/28:(1-3/28)=25/28:25/28=1
1=1⇒arctg3/4+arctg1/7=π/4
2)sin(arcsin0,8+arccos0,8)=sinπ/2
sin(arcsin0,8+arccos0,8)=1
sin(arcsin0,8)cos(arccos0,8)+cos(arcsin0,8)sin(arccosa)=
=0,8*0,8+√1-0,64*√1-0,64=0,64+0,6*0,6=0,64+0,36=1
1=1⇒arcsin0,8+arccos0,8=π/2
ОДЗ: х≠1
(x-2)²(x+4)(1-x)≥0
-(x-2)²(x+4)(x-1)≥0
(x-2)²(x+4)(x-1)≤0
x=2 x=-4 x=1
+ - + +
--------- -4 --------------- 1 ------------- 2 --------------
\\\\\\\\\\\\\\\\
x∈(-∞; -4) x= -5 + - - | +
x∈(-4; 1) x=0 + + - | -
x∈(1; 2) x=1.5 + + + | +
x∈(2; +∞) x=3 + + + | +
x∈[ -4; 1)U{2}
Ответ: [-4; 1)U{2}.
(c+3x)(c-3x)=c^2-9x^2
9x^2-(c^2-9x^2)=c^2+18x^2
<span>1) f(x)=3x/x+3+7cosx</span>
<span><span>f(x)=3+3+7cosx</span></span>
<span><span><span>f(x)=6+7cos0</span></span></span>
<span><span><span><span>f(x)=6+7*1</span></span></span></span>
<span><span><span><span>f(x) = 13</span></span></span></span>
Ответ:13
2)
<span>a) у=</span><span>√x^2+1/x</span>
y=x+1/x, D(y): x≠0
При х=1 ⇒ y=1+1/1=2 имеем точку (1; 2)
При х = -1 ⇒ у=-1+(-1)/1=-2 точка (-1; -2)
При х=2 ⇒ у=2+1/2=2+0,5=2,5 - точка (2; 2,5)
и так дальше
По точкам можно нариссовать график.