5
:
..
2013
1 
, .
>> x=2.3*10^(-2)
x =0.0230
>> y=pi
y =3.1416
>> r=sinh((x+log(y))^3/sqrt(abs(x-log(y))))*cosh((x+log(y))*sqrt(abs(x-log(y))))
r = 3.9913
2 , , , , (0,1) . : (3,3); (4,3); (3,4). .
(BCB 4 CT) A 4
>> a=rand(3,3)
a =
0.0462 0.6948 0.0344
0.0971 0.3171 0.4387
0.8235 0.9502 0.3816
>> b=rand(4,3)
b =
0.7655 0.4456 0.2760
0.7952 0.6463 0.6797
0.1869 0.7094 0.6551
0.4898 0.7547 0.1626
>> c=rand(3,4)
c =
0.1190 0.3404 0.7513 0.6991
0.4984 0.5853 0.2551 0.8909
0.9597 0.2238 0.5060 0.9593
>> d=(b*c*b-4*c')*a^4
d =
-1.6634 -3.2211 -1.7993
1.3949 2.8650 1.5856
-0.2301 -0.4798 -0.2121
-3.0224 -6.1127 -3.4038
:
>> A=det(a)
A =
0.2058
b c .. .
3 , , , . .
>> a=zeros(7)
a =
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0
>> a=a+diag(7*ones(6,1),1)
a =
0 7 0 0 0 0 0
0 0 7 0 0 0 0
0 0 0 7 0 0 0
0 0 0 0 7 0 0
0 0 0 0 0 7 0
0 0 0 0 0 0 7
0 0 0 0 0 0 0
>> a=a+diag(7*ones(6,1),-1)
a =
0 7 0 0 0 0 0
7 0 7 0 0 0 0
0 7 0 7 0 0 0
0 0 7 0 7 0 0
0 0 0 7 0 7 0
0 0 0 0 7 0 7
0 0 0 0 0 7 0
>> a=fliplr(a)
a =
0 0 0 0 0 7 0
0 0 0 0 7 0 7
0 0 0 7 0 7 0
0 0 7 0 7 0 0
0 7 0 7 0 0 0
7 0 7 0 0 0 0
0 7 0 0 0 0 0
>> a(1,:)=1:7
a =
1 2 3 4 5 6 7
0 0 0 0 7 0 7
0 0 0 7 0 7 0
0 0 7 0 7 0 0
0 7 0 7 0 0 0
7 0 7 0 0 0 0
0 7 0 0 0 0 0
>> a(:,1)=1:7
a =
1 2 3 4 5 6 7
2 0 0 0 7 0 7
3 0 0 7 0 7 0
4 0 7 0 7 0 0
5 7 0 7 0 0 0
6 0 7 0 0 0 0
7 7 0 0 0 0 0
>> a(7,:)=1:7
a =
1 2 3 4 5 6 7
2 0 0 0 7 0 7
3 0 0 7 0 7 0
4 0 7 0 7 0 0
5 7 0 7 0 0 0
6 0 7 0 0 0 0
1 2 3 4 5 6 7
>> a(:,7)=1
a =
|
|
|
1 2 3 4 5 6 1
2 0 0 0 7 0 1
3 0 0 7 0 7 1
4 0 7 0 7 0 1
5 7 0 7 0 0 1
6 0 7 0 0 0 1
1 2 3 4 5 6 1
4: :
1) 
>> syms x
>> limit((x^2-5*x-14)/(2*x^2 -9*x-35),7)
ans = 9/19
2) 
>> syms x
>> limit((8*x^3-1)/(x^2 -1/4),1/2)
ans = 6
3) 
>> syms x
>> limit((x^3-3*x^2+10)/(7*x^3 +2*x+1),inf)
ans = 1/7
>> syms x
>> limit((5*x^2-3*x+1)/(x^4 +2*x+1),inf)
ans = 0
>> syms x
>> limit((8*x^4+7*x^3-3)/(3*x^2-5*x+1),inf)
ans = Inf
6) 
>> syms x
>> limit((sqrt(3*x+17)-sqrt(2*x+12))/(x^2+8*x+15),-5)
ans = 0.707
7) 
>> syms x
>> limit(((x-7)/x)^(2*x+1),inf)
ans = 1/exp(1)^14
8) 
>> syms x
>> limit((sin(3*x)^2-sin(x)^2)/x^2,0)
ans = 8
5: 
.
:
1) 
: 
;
2) 
;
3) 
;
4) 
; 
;
5) , , 
;
6) ;
7) , , .
 ,
|  ,
|  .
|
>> a=[3 3 1]
a = 3 3 1
>> b=[1 -2 1]
b = 1 -2 1
>> c=[1 1 1]
c = 1 1 1
:
>> dl_a=sqrt(a(1)^2 + a(2)^2 +a(3)^2)
dl_a =4.3589
>> dl_b=sqrt(b(1)^2 + b(2)^2 +b(3)^2)
dl_b = 2.4495
:
>> sk_ab=dot(a,b)
sk_ab = -2
:
>> cos_ab=sk_ab/(dl_a*dl_b)
cos_ab = -0.1873
:
>> vek_ab=cross(a,b)
vek_ab = 5 -2 -9
:
>> smesh_abc=dot(cross(a, b), c)
smesh_abc = -6
, .
, ,
>> ab1=a(1)/b(1)
ab1 = 3
>> ab2=a(2)/b(2)
ab2 = -1.5000
>> ab3=a(3)/b(3)
ab3 = 1
ab1 ab2 ab3, .
:
.
>> Komp=[a(1) a(2) a(3);b(1) b(2) b(3);c(1) c(2) c(3)]
Komp =
3 3 1
1 -2 1
1 1 1
>> Kom=det(Komp)
Kom = -6.0000
, .
6: : 
, 
, 
. :
1. , .
2. .
3. .
4. .
5. , , .
6. .
7. .
| 
| 
| |
| (-3, 2) | (2, 5) | (-1, -2) |
, .
>> syms xh
>> syms yh
>> syms xp
>> syms yp
>> A=[-3;2]
A =
-3
>> B=[2;5]
B =
>> C=[-1;-2]
C =
-1
-2
, .
text='uravnenie ax+by+c=0, dlya AB:'
text =uravnenie ax+by+c=0, dlya AB:
>> a1=B(2)-A(2)
a1 = 3
>> b1=A(1)-B(1)
b1 = -5
>> c1=A(2)*B(1)-A(1)*B(2)
c1 = 19
>> text='uravnenie ax+by+c=0, dlya AC:'
|
|
|
text =uravnenie ax+by+c=0, dlya AC:
>> a2=C(2)-A(2)
a2 = -4
>> b2=A(1)-C(1)
b2 = -2
>> c2=A(2)*C(1)-A(1)*C(2)
c2 = -8
.
>> vectAB=[B(1)-A(1), B(2)-A(2)]
vectAB = 5 3
>> vectCH=[ xh - C(1); yh - C(2) ]
vectCH = xh + 1
yh + 2
>> 'koordinati tochki '
ans =koordinati tochki
>> M1=[B(1)-A(1), B(2)-A(2); a1, b1]
M1 =
5 3
3 -5
>> M2=[(B(1)-A(1))*C(1) + (B(2)-A(2))*C(2), B(2)-A(2); -c1, b1]
M2 =
-11 3
-19 -5
>> M3=[B(1)-A(1), (B(1)-A(1))*C(1) + (B(2)-A(2))*C(2); a1, -c1]
M3 =
5 -11
3 -19
>> xh=det(M2)/det(M1)
xh = -3.2941
>> yh=det(M3)/det(M1)
yh = 1.8235
>> text='uravnenie ax+by+c=0, dlya CH:'
text =uravnenie ax+by+c=0, dlya CH:
>> a3=yh-C(2)
a3 = 3.8235
>> b3=C(1)-xh
b3 = 2.2941
>> c3=C(2)*xh-C(1)*yh
c3 = 8.4118
>> 'koordinati tochki M'
ans =koordinati tochki M
>> xm=(B(1)+C(1))/2
xm = 0.5000
>> ym=(B(2)+C(2))/2
ym = 1.5000
>> text='uravnenie ax+by+c=0, dlya AM:'
text =uravnenie ax+by+c=0, dlya AM:
>> a4=ym-A(2)
a4 = -0.5000
>> b4=A(1)-xm
b4 = -3.5000
>> c4=A(2)*xm-A(1)*ym
c4 = 5.5000
>> text='dlina AM:'
text =dlina AM:
>> dl=sqrt((A(1)-xm)^2 + (A(2)-ym)^2)
dl = 3.5355
.
,
cos∠α = (b² + c² - a²) / 2 b c
text='dlini storon AB,AC,BC:'
text =dlini storon AB,AC,BC:
>> AB=sqrt((B(1)-A(1))^2 + (B(2)-A(2))^2)
AB = 5.8310
>> AC=sqrt((C(1)-A(1))^2 + (C(2)-A(2))^2)
AC = 4.4721
>> BC=sqrt((C(1)-B(1))^2 + (C(2)-B(2))^2)
BC = 7.6158
>> cosBAC=(AB^2 + AC^2 - BC^2) / (2*AB*AC)
cosBAC = -0.0767
>> ugolBAC=acos(cosBAC)
ugolBAC = 1.6476
