197
Yechish:
>> maple(‘solve’,’{(x-2)/(x+3)<=51, sqr(x) *(sqrt(x)-1) <10,10*x^2+4*x>=69}’,x)
ans =
{-1/5+1/10*694^(1/2)<= x, x < 21/2+1/2*41^(1/2)}
>> vpa(ans,4)
ans =
{2.434 <= x, x < 13.70 }
Tengsizliklar sistemasida aniq yechimi
- +
( )
≤ x, x<
+
( )
.
Va
taqribiy yechimi
2,434
≤ x <13,70
Sonli differensiallash va integrallash
Polinomning hosilasini hisoblashda polyder, funksiyaning
hosilasini hisoblashda
diff komandalaridan foydalanish mumkin.
1-misol. P(x)=x
5
+ x
3
+ 1 polinomning hosilasi.
>> P=[ 1 0 1 0 0 1 ];
% berilgan polinom koeffitsentlarining vektori
>> P1 (x) koeffitsentlarining vektori
P1 =
5 0 3 0 0
Yani P’ (x) = 5x
4
+ 3x
2
2-misol. Y = sin(x) funksiya hosilasining taqribiy qiymatini hisoblash.
>> x=0:.05:10;
%
argumentlar vektori
>>y=sin(x);
%funksiya qiymatlarining vektori
>>d=diff(y);
% qo’shni elementlar ayirmalarining vektori: d=[y(2)-y(1),…,y(n)-y(n-1)]
>>pr=d/0.05;
% hosila qiymatlarining vektori
>>pr(5)
%hosila x=x(5)=0.2
dagi qiymati
0.9747
>>cos(x(5))
% aniq qiymat bilan taqqoslash
0.9801
Funksiyaning hosilasini hisoblash uchun trapetsiyalar va Simson usullariga mos
keluvchi trapz va quad komandalaridan foydalaniladi.
198
∙ 3-misol. f (e 2x - 1) dx integralni trapetsiyalar
va Simpson usullari bilan
hisoblash.
1 – trapetsiyalar usuli:
>> h=0.001; x=0:h:1;
>> y=exp(2*x)-1;
>> int=trapz(y)*h
Int=
2.1945
2 – Simpson usuli:
>> int=quad(‘exp(2*x)-1’,0,1,1.0e-5)
Int = 2.1945
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