Задачи по "Математике"

Вариант 23

f(x)=cos⁡(x^2-1)- √(x^3 )+5

df/dx(x_n ) =[f(x_n )-f(x_(n-1) )]×1/(x_n-x_(n-1) )

x_(n+1)=x_n- (x_n-x_(n-1))/(f(x_n )-f(x_(n-1) ) ) f(x_n)

Находим вторую производную:

(d^2 F)/(dx^2 )=-(4x^2 cos⁡(x^2-1)+2 sin⁡(x^2-1)+3√(x^3 ))/4x^2

интервал [2.8, 3.4] разобьем на 10 подынтервалов.

h 1 = 2.8 + 1×(3.4 – 2.8)/10 =2.86

h 2 = 2.8 + (1+1) ×(3.4 – 2.8)/10 = 2.92

f(2.8) = -3.836, f(3.4) = -6.691

x = 2.96

Задание 2

y’= 2y/(x+1)+e^x×(x+1)^2

y(a) = 1 a=0 b=2

y(x)=〖(x+1)〗^2×e^x

Yі+1= yі+h ×f (xі,yі)

y(x)=〖(x+1)〗^2×e^x в виде yt=f(x;y)

f(x;y) = 〖(x+1)〗^2×e^x

x0 = 0, y0= 1

f(x0 y0) = f (0,1)= (0+1)2× 2.7=1

hf (x0 y0)= 0,1×1= 0.1

x1=0,1

y1= y0 + hf (x0 y0) =1+0.1=1.1

f(x1 y1)=f(0,1;1,1) = (0.1+1)2 × 2.70.1= 2.31

hf (x1 y1)=0,1×2.31= 0.231

x2=0,2

y2 = y1+hf(x1;y1)=1.1+0.231=1.331

f(x2 y2)=f(0,2;1,331)= (0.2+1)2 × 2.70.2=2.659

hf (x2 y2)= 0,1×2.659=0.2659

x3=0.3

y3=y2+ hf(x2;y2)=1.331+0.2659=1.5969

f(x3 y3)=f(0,3;1,5969)= (0.3+1)2 × 2.70.3=3.037

hf (x3 y3)= 0,1×3.037=0.3037

x4=0.4

y4=y3+ hf(x3;y3)=1.5969+0.3037=1.9006

f(x4 y4)=f(0,4;1,9006)= (0.4+1)2 × 2.70.4=3.447

hf (x4 y4)= 0,1×3.447=0.3447

x5=0.5

y5=y4+ hf(x4;y4)= 0.3447+1.9006=2.2453

f(x5 y5)=f(0,5;2.2453)= (0.5+1)2 × 2.70.5=3.893

hf (x5 y5)= 0,1×3.893=0.3893

x6=0.6

y6=y5+ hf(x5;y5)= 0.3893+2.2453=2.6346

f(x6 y6)=f(0,6; 2.6346)= (0.6+1)2 × 2.70.6=4.374

hf (x6 y6)= 0,1×4.374=0.4374

x7=0.7

y7=y6+ hf(x6;y6)= 0.4374+2.6346=3.072

f(x7 y7)=f(0,7; 3.072)= (0.7+1)2 × 2.70.7=4.894

hf (x7 y7)= 0,1×4.894=0.4894

x8=0.8

y8=y7+ hf(x7;y7)= 0.4894+3.072=3.561

f(x8 y8)=f(0,8; 3.561)= (0.8+1)2 × 2.70.8=5.453

hf (x8 y8)= 0,1×5.453=0.5453

x9=0.9

y9=y8+ hf(x8;y8)= 0.5453+3.561=4.1063

f(x9 y9)=f(0,9; 4.1063)= (0.9+1)2 × 2.70.9=6.054

hf (x9 y9)= 0,1×6.054=0.6054

x10=1

y10=y9+ hf(x9;y9)= 0.6054+4.1063=4.7117

f(x10 y10)=f(1; 4.7117)= (1+1)2 × 2.71=6.7

hf (x10 y10)= 0,1×6.7=0.67

Вариант