:
- C - , - , - :
MN - , :
(-2;8); (2;-2)
. k b y=kx+b, :
8 = -2k+b 8 = -2k-2-2k 4k =-10 k = -2,5
-2 = 2k+b b = -2-2k b =-2-2k b = 3
y = -2,5x+3 :
y = -2,5x+3
2,5+-3=0
: 2,5+-3=0
2. :
) )
) = = =
= = = 2
) =
3
= =
: u=1/x
= = = -
3. :
) ; ) ; ) .
) = - + = - + 3x + C
) = 8 = 8 ln x + C
) = + = +
u=5x.
du=5dx dx=du/5:
+ = + = + sin(u)+C= + sin(5x)+C
4. : = 33
Y
Y, x 0:
x = 0 33 .
3⋅ 03− 0=0
f(0)=0
: (0, 0)
X
X, y 0:
y = 0 y=3x3 - x.
3 x3−x =0
x(3 x2−1) =0
x1=0; (3 x2−1) =0
x2=
x3=-
: (0, 0); (,0); (- ,0).
, ,
f ′(x)=0 ( ),
:
f ′(x)=(3 x3−x)′ = 9x2 1
9x2 1 = 0
, :
x1=− ;
x2= .
: (− ; ); (; - )
.
, , , :
x1= ;
x2=− .
(- ∞; − ] U [∞; )
[ − ; ]
,
f ′′(x)=0 ( ),
,
f ′′(x)= (3 x3−x)′′= (9x2 1)′ = 18x
18x=0
, :
x=0
.
, , , :
[ 0, ∞)
(-∞, 0 ]
x→∞ x→ - ∞
(3x3-x)= - ∞ ,
.
(3x3-x)= ∞ ,
.
|
|
, 3x3-x, x x→∞ x→ - ∞
= ∞ ,
.
= ∞ ,
.
f = f(-x) f = -f(-x).
, :
3x3-x = -3 x3+x
3x3-x = -(-3 x3+x)
, , .
5. :
(0)=5
:
, :
ln(y+1) = ln(x+2) + ln(C)
y = C (x+2) 1
(0)=5
5 = C (0+2) 1
=(5+1)/2
=3
y = 3 (x+2) 1
y = 3x+6 1
y = 3x+5