, . , , . , .
>> ch1=(xp-C(1))/(B(1)-A(1))
ch1 = xp/5 + 1/5
>> ch2=(yp-C(2))/(B(2)-A(2))
ch2 = yp/3 +2/3
>> text='uravnenie iskomoy pryamoy (levaya chast):'
text =uravnenie iskomoy pryamoy (levaya chast):
>> ch1-ch2
ans = xp/5 - yp/3 7/15
.
2 .
>> text='naidem koordinati tochki peresecheniya, reshiv sistemu iz 2 uravneniy pryamih'
text =naidem koordinati tochki peresecheniya, reshiv sistemu iz 2 uravneniy pryamih
>> D1=[a3, b3; a4, b4]
D1 =
3.8235 2.2941
-0.5000 -3.5000
>> D2=[-c3, b3; -c4, b4]
D2 =
-8.4118 2.2941
-5.5000 -3.5000
>> D3=[a3, -c3; a4, -c4]
D3 =
3.8235 -8.4118
-0.5000 -5.5000
>> xt=det(D2)/det(D1)
xt = -3.4375
>> yt=det(D3)/det(D1)
yt = 2.0625
.
( )
p=(a+b+c)/2
>> text='ploshad` ABC:'
text =ploshad` ABC:
>> p=(AB+AC+BC)/2
p = 8.9594
>> SABC=sqrt(p*(p-AB)*(p-AC)*(p-BC))
SABC = 13.0000
7:
1)
) ; ) .
) :
>> D=[2 -1 2;1 1 2;3 1 4]
D =
2 -1 2
1 1 2
3 1 4
>> D1=[8 -1 2;11 1 2;22 1 4]
D1 =
8 -1 2
11 1 2
22 1 4
>> D2=[2 8 2;1 11 2;3 22 4]
D2 =
2 8 2
1 11 2
3 22 4
>> D3=[2 -1 8;1 1 11;3 1 22]
D3 =
2 -1 8
1 1 11
3 1 22
>> detD=det(D)
detD = -2.0000
>> x1=det(D1)/detD
x1 = 3.0000
>> x2=det(D2)/detD
x2 = 3
>> x3=det(D3)/detD
x3 = 2.5000
) :
>> A=[2 -1 2 8;1 1 2 11;3 1 4 22]
A =
2 -1 2 8
1 1 2 11
3 1 4 22
>> rref(A)
ans =
1.0000 0 0 3.0000
0 1.0000 0 3.0000
0 0 1.0000 2.5000
2)
) ; ) .
>> D=[3 1 -2;5 -3 2;-2 5 -4]
D =
3 1 -2
5 -3 2
-2 5 -4
>> D1=[6 1 -2;4 -3 2;0 5 -4]
D1 =
6 1 -2
4 -3 2
0 5 -4
>> D2=[3 6 -2;5 4 2;-2 0 -4]
D2 =
3 6 -2
5 4 2
-2 0 -4
>> D3=[3 1 6;5 -3 4;-2 5 0]
D3 =
3 1 6
5 -3 4
-2 5 0
>> detD=det(D)
detD = -16
>> x1=det(D1)/detD
x1 = 0.7500
>> x2=det(D2)/detD
x2 = -2
>> x3=det(D3)/detD
x3 = -2.8750
) :
>> A=[3 1 -2 6;5 -3 2 4;-2 5 -4 0]
A =
3 1 -2 6
5 -3 2 4
-2 5 -4 0
>> rref(A)
ans =
1.0000 0 0 0.7500
0 1.0000 0 -2.0000
0 0 1.0000 -2.8750
3)
|
|
|
>>A=[2 5 1;4 6 3; 1 -1 -2]
2 5 1
4 6 3
1 -1 -2
>> syms x1 x2 x3
>> y1=2*x1+5*x2+x3;
>> y2=4*x1+6*x2+3*x3;
>> y3=x1-x2-2*x3;
>> S=solve(y1,y2,y3,x1,x2,x3)
S = x1: [1x1 sym]
x2: [1x1 sym]
x3: [1x1 sym]
>> disp([S.x1 S.x2 S.x3])
[ 0, 0, 0]
8: . 1- , 2 3, 4 5, 3 5 - 1.
1) 
>> syms x
>> diff((4/x^5-9/x+x^(2/5)-7*x^3),2)
ans = 120/x^7-18/x^3-6/25/x^(8/5)-42*x
2) 
>> syms x
>> diff((4*x^2-3*x-4)^(1/3)-2/(x-3)^5,3)
ans = 10/27/(4*x^2-3*x-4)^(8/3)*(8*x-3)^3-16/3/(4*x^2-3*x-4)^(5/3)*(8*x-3)+420/(x-3)^8
3) 
>> syms x
>> diff(exp(x)^(-sin(x))*tan(7*x^6),1)
ans = exp(x)^(-sin(x))*(-cos(x)*ln(exp(x))-sin(x))*tan(7*x^6)+42*exp(x)^(-sin(x))*(1+tan(7*x^6)^2)*x^5
4) -----
5) 
>> syms x
>> diff((x+2)^7*acos(sqrt(x)),1)
ans= -(2+x)^7/(2*sqrt(-(-1+x) x))+7*(2+x)^6*acos*(sqrt(x))
9: . ( , )
:
>> f1=x^2+1
f1 = x^2+1
>> f2=2*x
f2 =2* x
>> f3=x+2
f3 =x+2
>> syms x
>> k1=limit(f1,x,1,'left')
k1 =2
>> k2=limit(f2,x,1,'right')
k2 =2
>> if(k1==k2)
'funkcij nepreruvna'
else
'funkcij ne nepreruvna'
end
ans =funkcij nepreruvna
>> k3=limit(f2,x,3,'left')
k3 =6
>> k4=limit(f3,x,3,'right')
k4 =5
>> if(k3==k4)
'funkcij nepreruvna'
else
'funkcij ne nepreruvna'
end
ans =funkcij ne nepreruvna
:
>> x1=-10:1:1;
x2=1:1:3;
x3=3:1:10;
y1=x1.^2+1;
y2=2.*x2;
y3=x3+2;
plot(x1,y1,x2,y2,x3,y3) 
. .
>> x1=-5;
>> x2=-4;
>> f=(x-3)*(x+4);
>> syms x
>> k1=limit(f,x,x1,'left')
k1 =8
>> k2=limit(f,x,x1,'right')
k2 =8
>> if(k1==k2)
'funkcij nepreruvna'
else
'funkcij ne nepreruvna'
end
ans =funkcij nepreruvna
>> k1=limit(f,x,x2,'left')
k1 =0
>> k2=limit(f,x,x2,'right')
k2 =0
>> if(k1==k2)
'funkcij nepreruvna'
else
'funkcij ne nepreruvna'
end
ans =funkcij nepreruvna
