Lab_4
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I ( goto ( / + 8+- ( F+ , 7 ! 7 , 8 / .
> ( ( / 8 ( . > ( + 8 8 , + ( , ( / ( ! ( ( ( : break continue .
3. 0 1 . 2 34 $ – 56 1 #$.
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y ≥ x2 |
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l o w e r = 0 u p p e r = 3 0 0 s t e p = 1 0 |
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s u m :)= 1 |
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+ 8 |
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i : = 2 |
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f a h r = l o w e r |
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c e l s i u s = 5 . / 9 . * ( f a h r - 3 2 . 0 ) |
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) |
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f a h r = f a h r + s t e p |
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f a h r < = u p p e r |
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; |
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#include <stdio.h> |
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void main() |
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{ |
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int lower=0,upper=300,step=10; |
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float fahr,celsius; |
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printf(" |
Таблиця відповідності температур по Фарангейту \n "); |
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printf(" |
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температурам по Цельсію. \n "); |
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printf("| |
Фарангейт |
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Цельсію | \n "); |
fahr=lower; |
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while(fahr<=upper) |
{ celsius=5./9.*( fahr-32.0); |
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printf("| |
%4.0 |
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%6.1 |\n ",fahr,celsius); |
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fahr+=step; |
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}
}
! 3. I + n. O (+ 8 8+ ++ 1 n, 8 12 22 32 42 ... n2.
4
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© . . |
.
) n
m u l:= 1
i:= 2
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m u l:= m u l* i2 |
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+ |
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i< n |
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i:= i+ 1 |
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)m u l
#include<iostream.h> void main()
{
int n,i; double mul;
cout<<" Введіть натуральне число n"; cin<<n;
mul:=1;
for( i=2;i<= n; i++ ) mul*=i*i; cout<<" Добуток квадратів перших "<<n;
cout<<" натуральних чисел дорівнює ="<<mul;
}
. 4. I + |
n x. "8 ε = 0.001 |
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100 |
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s=1 s!(n + s)! 2s +1 |
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#include <stdio.h> |
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#define |
EPSILON 0.001 |
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#define |
MAXSUM 100 |
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void main() |
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{ |
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int n,s, |
i,j,fs,fsn; |
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double x , px,Summa; |
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printf(" Введіть натуральне число n та дійсне число x \n "); |
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scanf("%d%lf" ,&n,&x); |
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fs=1;fns=1; Summa=0; |
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for(i=2; i<=n; i++) fns*=i; |
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for(s=1; s<=MAXSUM; s++) { |
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fsn*=(s+n); |
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fs*=s; |
px=1; |
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for(i=1; i<=2*s+n; i++) px*=(x/(2*s+n)); |
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px/=(fs*fsn); |
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Summa+=px; if(fabs(px)<EPSILON) break;
}
printf(" Результат %f з точністю EPSILON. \n ",Summa);
}
5. 2 1 3$; 3 6 ! 5 #4$5 <.
5
’ – ++ |
© . . |
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. + , 7 + |
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/ . |
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. 5. I + + xn = 1.25xn−1 + 0.125, x0 = 1. O |
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8-(+ (+ / n - |
+ |
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x n 1 = 1 , 0 |
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i : = |
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x n = 1 . 2 5 x n 1 + 0 , 1 2 5 |
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x n 1 = x n |
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i < n |
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; |
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#include <iostream> |
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using namespace std; |
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void main() |
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{ |
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int n,i; |
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double xn,xn1; |
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do { |
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cout<<"Input n \n"; |
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cin>>n; |
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} while(n<=1); |
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xn1=1.0; |
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for(i=1;i<n;i++) |
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{ |
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xn=1.25*xn1+0.125; |
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xn1=xn; |
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} |
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cout<<" x ("<<n<<")="<<xn<<endl; |
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} |
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. 6. I + |
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xn = 1.25xn−1 + 0.125yn−1, |
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x0 = 1, |
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yn = 1.25yn−1 + 0.125xn, |
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y0 = 0, |
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_ n (+ / yn - + .
#include <iostream> using namespace std; void main()
{
int n,i;
double xn,xn1; double yn,yn1;
6
’ – ++ |
© . . |
do { cout<<"Input n \n";
cin>>n; } while(n<=0);
xn1=1.0;
yn1=1.0; for(i=0;i<n;i++)
{
xn=1.25*xn1+0.125*yn1;
yn=1.25*yn1+0.125*xn;
xn1=xn;
yn1=yn;
}
cout<<" y ("<<n<<")="<<yn<<endl;
}
. 7. I + + xn = 1.25xn−1 + 0.125, x0 = 1.
_ [5,8] [10,14], +( ( + , / (.
#include <iostream> using namespace std; void main()
{
double xn, Sum1,Sum2; Sum1=0; Sum2=0;
xn=1.0; while(1)
{
xn=1.25*xn+0.125; if( xn>14 ) break;
if( xn>=10) Sum2+=xn; if( xn>8) continue; if( xn<=5) Sum1+=xn;
}
cout<<" Summa [5,8] = "<<Sum1<<" Summa [10,14] = "<<Sum2<<endl;
}
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. / 0 / |
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= 4 > 1. |
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1.1. |
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I |
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+ |
n. > (+ 8 |
8+ + |
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+ |
1 n, 8 n!=1 2 3 4 ... n. |
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1.2. |
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I + |
n. > (+ 8 + : |
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1 2 + |
2 2 + 3 2 + |
4 |
2 + ... + n 2 |
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1 2 3 4 |
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... n |
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1.3.I + n x. > (+ 8
+ : cos x + cos3x + cos5x + ... + cos(2 n + 1) x.
1.4.I + n x. > (+ 8+ : ln 2x + ln 4x + ln 6x + ... + ln 2nx
1.5.I + n x. > (+ 8
+ : tgx + tg9x + tg17x + ... + tg(8n +1)x .
1.6.I + n x. > (+ 8
+ : xtgx + 2xtg3x + 3xtg5x +...+ nxtg(2n −1)x.
1.7. I + n. > (+ 8 + :
e0 + e1 + e2 + e3 + ...+ en . 1 2 3 4 ... n
1.8. I + n. > (+ 8 + :
1+ |
1 |
+ |
1 |
+ |
1 |
+ ... + |
1 |
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2 |
22 |
23 |
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2n |
7
’ – ++ |
© . . |
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1.9. |
I + n. > (+ 8 + : |
e0 + e1 + e2 + e3 + ... + en . 1 2 3 4 ... n
1.10. I + n. > (+ 8 + :
1+ |
1 |
+ |
1 |
+ |
1 |
+ ... + |
1 |
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2 |
22 |
23 |
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2n |
1.11.I + n x. > (+ 8
+ : x + x 2 + x3 + ... + x 2n .
1.12. |
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I + |
n. > (+ 8 + : |
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+ ... + |
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1.13. |
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I + |
n. > (+ 8 + : |
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+ |
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+ |
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+ ... + |
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nln(n +1) |
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1ln 2 |
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2ln3 |
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3ln 4 |
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1.14.I + n. > (+ 8 + :
cos1 |
+ |
cos2 |
+ |
cos3 |
+ ... + |
cos n |
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1 2 2 3 3 4 |
n (n +1) |
1.15.I + n. > (+ 8 + :
sin 2 |
+ |
sin |
3 |
+ |
sin |
4 |
+ ... + |
sin n |
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(n −1) n (n +1) |
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1 2 3 2 3 4 3 4 5 |
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= 4 > 2.
2.1.> + + 8 F+ y = x3 [2,5] ( 0.5.
2.2. |
I n>0. > + + 8 F+ y = |
x2 |
− 7 |
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2 |
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[0, n ] ( 0.5. |
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2.3. |
I n>0. > + + 8 F+ |
y = xsin(x) |
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[0, n ] ( 1. |
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2.4. |
I h>0. > + + 8 F+ y = cos(x) |
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[0,π ] ( h. |
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2.5. |
I b>0 h>0. > + + 8 F+ y = ex |
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[0, b] ( h. |
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2.6. |
I a, b h (b>a,h>0). > + + 8 F+ |
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y = tg(x) [a, b] ( h. |
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2.7. |
I a, b h(b>a,h>0). > + + 8 F+ |
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y = xe−x [a, b] ( h. |
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y = |
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ex |
+ e |
− x |
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2.8. |
I n>0. > + + 8 F+ |
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2.9. |
I n>0. > + + 8 F+ |
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[0, n ] ( 0.5. |
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2.10. |
I n>0. > + + 8 F+ |
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2.11. |
I h>0. > + + 8 F+ y = arctg(x) |
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[0, 3 ] ( h. |
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2.12. |
I a b(b>a). > + + 8 F+ |
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y = 5 x3 − 2 x [a, b] ( 0.1. |
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© . . |
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2.13. |
I n>0. > + + 8 F+ y = x5 − x3 + x |
[-n, n ] ( 2.
2.14. I h>0. > + + 8 F+ y = (π − x)tg(x) [0, π ] ( h.
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4 |
2.15. I h>0. > + + 8 F+
y = (π − 2x)tg(2x) [0, π ] ( h.
2 8
= 4 > 3.
3.1. _ + n x. > (+ 8 +( ε = 0.001:
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3.2. _ + x 8 ε . > (+ 8 +(+ :
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3.3. _ + n x 8 ε . > (+ 8 +(+ :
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9
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© . . |
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= 4 ># 4-6 . |
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J K L ! ! -"# . |
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1 1 |
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1. I + + xn = xn−1 + 0.5, |
x0 = −5. > (+ |
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2. I + |
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xn = 1.5xn−1 − 0.25yn−1, |
x0 = 1, |
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yn = 1.05yn−1 +1.025xn, |
y0 = 0.5, |
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3. I + + xn = xn−1 + 0.5, |
x0 = −5. |
_ [5,12] [18,22], +( ( + , / (.
1 2 |
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1. |
I + + xn = xn−1 + 0.5xn−2, x0 = 1, |
x1 = 2. |
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2. |
I + |
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xn = 1.75xn−1 − 0.275yn−1, |
x0 = 1.25, |
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yn = 1.05yn−1 +1.025xn −1.05, |
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3. |
I + + xn = xn−1 + 0.5xn−2 + 0.25, |
x0 = 0.5, |
x1 = 0.75. |
_ [5,12] [30,38], +( ( + , / (.
1 3. |
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+ + xn = axn−1 + 0.5xn−2, x0 = 1, x1 = a. |
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y0 = 0.5 . |
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3. |
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(a>0) ,b,(c>0),d(d>2*c) + + |
xn = xn−1 + axn−2 + 0.25, x0 = 0.5*b, x1 = 0.75.
_ [c,2*c] [d,3*d], +( ( + , / (.
1 4. |
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1. |
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xn = axn−1 + 0.25xn−2 − 0.25a, |
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2. |
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x0 = 1.5*b, |
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3. |
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(a>3) , b (b > a) + + |
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xn = 0.5xn−1 + 0.1axn−2 + 0.1bxn−3 + 0.25a, x0 = 0.25, |
x1 = 0.75, x2 = 0.51. |
I +(+ ( , / ( [0, 1+ ], [3+2 ,3+5*b] [100+5*b, +∞ [.
10