Ўзбекистон республикаси ахборот технологиялари ва коммуникацияларини

4). Берилган 
]
2
/
;
2
/
[



оралиқда аргумент ихтиёрий 
х
- учун
функциянинг қийматларини Лагранж интерполяцион формуласида 
ҳисоблаймиз.  




































1
10
1
9
1
8
1
7
1
6
1
5
1
4
1
3
1
2
1
10
9
8
7
6
5
4
3
2
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
L
n

---

60 




































2
10
2
9
2
8
2
7
2
6
2
5
2
4
2
3
2
1
2
10
9
8
7
6
5
4
3
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
 




































3
10
3
9
3
8
3
7
3
6
3
5
3
4
3
2
3
1
3
10
9
8
7
6
5
4
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
 




































4
10
4
9
4
8
4
7
4
6
4
5
4
3
4
2
4
1
4
10
9
8
7
6
5
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































5
10
5
9
5
8
5
7
5
6
5
4
5
3
5
2
5
1
5
10
9
8
7
6
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































5
10
5
9
5
8
5
7
5
6
5
4
5
3
5
2
5
1
5
10
9
8
7
6
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































6
10
6
9
6
8
6
7
6
5
6
4
6
3
6
2
6
1
6
10
9
8
7
5
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































7
10
7
9
7
8
7
7
6
5
7
4
7
3
7
2
7
1
7
10
9
8
6
5
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































8
10
8
9
8
7
8
6
8
5
8
4
8
3
8
2
8
1
8
10
9
7
6
5
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x




































9
10
9
8
9
7
9
6
9
5
9
4
9
3
9
2
9
1
9
10
8
7
6
5
4
3
2
1
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
;
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
)
(
10
9
10
8
10
7
10
6
10
5
10
4
10
3
10
2
10
1
10
9
8
7
6
5
4
3
2
1
y
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x



































5
.
0

x
нуқтада функциянинг қийматларини ҳисоблаш учун формуладаги
i
x
ва 
i
y


10
..
1

i
ўрнига унинг қийматларни қуйамиз ва ҳисоблаш 
натижасида функциянинг тақрибий қиймати 
1
.229853743
0
)
5
.
0
(

f
ни топамиз. 
5). а). 
)
(
sin
2
x
y

функциянинг Maple тилидаги графиги. 
>
plot(sin(x)^2,x=-1.57..1.57,color=red); 

---

61 
 
б). Берилган жадвал асосида Лагранж интерполяцион формуласи 
ёрдамида топилган функциянинг Maple тилидаги графиги чизиш дастури. 
 
> u:=proc(z)local s,s1,s2,i,k,x,y;x:=array(1..10);y:=array(1..10); 
x:=[-1.2566,-0.9425,-0.6283,-0.3142,0.0,0.3142,0.6283,0.9425,1.2566
,1.5708]; y:=[0.9045,0.6545,0.3455,0.0955,0.0,0.0955,0.3455,0.6545,0.9045,1.0];
s:=0; for i to 10 do
s1:=1; s2:=1; for k to 10 do if i<>k then s1:=s1*(z-x[k]); s2:=s2*(x[i]-
x[k]);fi; od; 
s:=s+s1/s2*y[i]; od;return(s) end; 
u
z