Предмет: Алгебра,
автор: апплпкпщкп
Сделайте пожалуйста!!!Дам 40 баллов!!!
Приложения:
Ответы
Автор ответа:
0
Формула трапеции
![intlimits^b_a { f(x) } , dx =h( frac{y_0+y_n}{2} +y_1+y_2+...+y_{n-1})+R_n;\ R_n leq frac{h^2}{12} (b-a)M_2, M_2= max_{[a;b]} [f'(x)]](https://tex.z-dn.net/?f=intlimits%5Eb_a+%7B+f%28x%29+%7D+%2C+dx+%3Dh%28+frac%7By_0%2By_n%7D%7B2%7D+%2By_1%2By_2%2B...%2By_%7Bn-1%7D%29%2BR_n%3B%5C+R_n+leq+frac%7Bh%5E2%7D%7B12%7D+%28b-a%29M_2%2C++M_2%3D+max_%7B%5Ba%3Bb%5D%7D+%5Bf%27%28x%29%5D "intlimits^b_a { f(x) } , dx =h( frac{y_0+y_n}{2} +y_1+y_2+...+y_{n-1})+R_n;\ R_n leq frac{h^2}{12} (b-a)M_2, M_2= max_{[a;b]} [f'(x)]")
![h= frac{b-a}{n} = frac{1-0}{10}=0,1 \
x_0=0, x_1=0,1, x_2=0,2, x_3=0,3, x_4=0,4, x_5=0,5, x_6=0,6\
x_7=0,7, x_8=0,8, x_9=0,9, x_{10}=1\
y_0=1, y_1= frac{100}{101}, y_2= frac{100}{104}, y_3= frac{100}{109}, y_4= frac{100}{116}, y_5= frac{100}{125}, y_6= frac{100}{136}, \
y_7= frac{100}{149}, y_8= frac{100}{164}, y_9= frac{100}{181}, y_{10}= frac{1}{2}\](https://tex.z-dn.net/?f=+h%3D++frac%7Bb-a%7D%7Bn%7D+%3D+frac%7B1-0%7D%7B10%7D%3D0%2C1+%5C%0Ax_0%3D0%2C++x_1%3D0%2C1%2C++x_2%3D0%2C2%2C++x_3%3D0%2C3%2C++x_4%3D0%2C4%2C++x_5%3D0%2C5%2C++x_6%3D0%2C6%5C%0Ax_7%3D0%2C7%2C++x_8%3D0%2C8%2C++x_9%3D0%2C9%2C++x_%7B10%7D%3D1%5C%0Ay_0%3D1%2C++y_1%3D+frac%7B100%7D%7B101%7D%2C++y_2%3D+frac%7B100%7D%7B104%7D%2C++y_3%3D+frac%7B100%7D%7B109%7D%2C++y_4%3D+frac%7B100%7D%7B116%7D%2C++y_5%3D+frac%7B100%7D%7B125%7D%2C+y_6%3D+frac%7B100%7D%7B136%7D%2C++%5C%0Ay_7%3D+frac%7B100%7D%7B149%7D%2C++y_8%3D+frac%7B100%7D%7B164%7D%2C++y_9%3D+frac%7B100%7D%7B181%7D%2C+y_%7B10%7D%3D+frac%7B1%7D%7B2%7D%5C "h= frac{b-a}{n} = frac{1-0}{10}=0,1 \
x_0=0, x_1=0,1, x_2=0,2, x_3=0,3, x_4=0,4, x_5=0,5, x_6=0,6\
x_7=0,7, x_8=0,8, x_9=0,9, x_{10}=1\
y_0=1, y_1= frac{100}{101}, y_2= frac{100}{104}, y_3= frac{100}{109}, y_4= frac{100}{116}, y_5= frac{100}{125}, y_6= frac{100}{136}, \
y_7= frac{100}{149}, y_8= frac{100}{164}, y_9= frac{100}{181}, y_{10}= frac{1}{2}\")
![intlimits^1_0 {frac{1}{1+x^2}} , dx =0,1( frac{1+ frac{1}{2}}{2}+ frac{100}{101}+ frac{100}{104} + frac{100}{109}+ frac{100}{116}+frac{100}{125}+ frac{100}{136} +frac{100}{149}+ frac{100}{164} +\+frac{100}{181} )+R_{10}=0,1( 0,75+0,99+0,9615+0,9174+0,862+0,8+\+0,7353+0,6711+0,6098+0,5525)=0,78\](https://tex.z-dn.net/?f=intlimits%5E1_0+%7Bfrac%7B1%7D%7B1%2Bx%5E2%7D%7D+%2C+dx+%3D0%2C1%28+frac%7B1%2B+frac%7B1%7D%7B2%7D%7D%7B2%7D%2B+frac%7B100%7D%7B101%7D%2B+frac%7B100%7D%7B104%7D+%2B+frac%7B100%7D%7B109%7D%2B+frac%7B100%7D%7B116%7D%2Bfrac%7B100%7D%7B125%7D%2B+frac%7B100%7D%7B136%7D+%2Bfrac%7B100%7D%7B149%7D%2B+frac%7B100%7D%7B164%7D+%2B%5C%2Bfrac%7B100%7D%7B181%7D+%29%2BR_%7B10%7D%3D0%2C1%28+0%2C75%2B0%2C99%2B0%2C9615%2B0%2C9174%2B0%2C862%2B0%2C8%2B%5C%2B0%2C7353%2B0%2C6711%2B0%2C6098%2B0%2C5525%29%3D0%2C78%5C "intlimits^1_0 {frac{1}{1+x^2}} , dx =0,1( frac{1+ frac{1}{2}}{2}+ frac{100}{101}+ frac{100}{104} + frac{100}{109}+ frac{100}{116}+frac{100}{125}+ frac{100}{136} +frac{100}{149}+ frac{100}{164} +\+frac{100}{181} )+R_{10}=0,1( 0,75+0,99+0,9615+0,9174+0,862+0,8+\+0,7353+0,6711+0,6098+0,5525)=0,78\")
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