-.
I : .
1. (, ,
). :
2. ( -
):
3. (.. )
: A * X = B; X * A = B; A * X * B = C,
A = 
; B = 
; C = 
;
4. , :
; 
II . .
1. a b: │a │= 2, │b │ = 3, (a, ^ b) = 60.
, : ,
c = (a + 3b) d = (2a - b),
c d. .
2. : │c│ = │3a - 2b│ = 5, │d │= │-5a + 6b│ = 4, (c, ^ d) = 2π /6. -
a b. .
3. t a = i + j + t k, b = i+ j + (t+1) k,
c = i j 2 t k ) ? ) 5 . .?
4. : A (3, 0), B (-1, 2), C (2, 5).
D , , | AB | = 3 | CD |
AB || CD. .
5. : │a │= 11, │b │ = 2 3, | a + b | = 30.
| a b |. .
6. p, q = { 2, 2, -1 }
3 k.
7. a, b = { 1,1,1 }
c = { 1, 3, -1 } j.
8. b, i, j,
a = { 4, - 3, 5 } , 2 | a |.
III . .
1. : (7; 2), B (1; 9), C (- 8; - 11). :
) , ∆ - ;
) ; -;
) K BD;
) CF F;
3. : A(0, 4, 3), B (4, 8, 1), C (2, 15, - 7), D (0, 6, 4).
, :
) ABC;
) ;
) AE;
) (≈ ) CD ACD;
4. ) : -4 x + 5 y + 20 = 0.
. 2 x + 5 = 0.
.
) : x + 3 y 2 z + 1 = 0 - 2 x + y + 3 z + 6 = 0.
|
|
|
4 x + 2 y + 6 z 3 = 0.
5. ; ,
; ; :
; 
; 
.
IV . .
1. ( !)
lim (x3-2x-1) / (5x4 + 4x+1);
x→ -∞
lim (16 + 5 x) 2/ (x + 3) ; lim (cos (7x) cos (3x)) / (π x) 2 ;
x→ - 3 x→ π
2. 
x 
.
3. , Y= f(x) x0:
Y=5x2-1,x0=6; Y=5x2+3,x0=8 .
4. :
; 
; 
V . .
1. :
__________
1. ) y = (5x 6) / (√ x 3 + 5x - 6); ) y = [ (3 ) ctg (1 2x) + ln [ sin (x/2) ] 4 ;
___________________
) y = log3 [ (√ (4x2 + 1) / (1 8x3) ]; ) y = [ arctg (2x+1) ] ln (cos x).
2. :
3. 1- 2- ,
4. y´ (x)
5. :
.
6. ,
.
7. 
.
8. 1- 2 - to = 1
y (x), :
_____
x (t) = arctg 2t, y (t) = ln [(√ t 2 + 2)/ (2 t+ 1)].
9. 1 - ( ):
f (x) = (sin x) arccos (ln2x)
10. 1 xo = 1
y (x), :
ln (2 y 2 + x ) = 4 x 2 y 3 18.
11. (
): ____
√ 22; lg 13.
12. y = (3x 4) (e) x - 2 .
VI . .
1. : a) 
, 
2. dz ( 
)
3. : 
4. : 
5. (1.1.3): 
