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anonymous
 5 years ago
Solve sinx=x^2 correct to four decimals using Newton's method with x sub zero=1.
anonymous
 5 years ago
Solve sinx=x^2 correct to four decimals using Newton's method with x sub zero=1.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Newton's method was developed to find the roots of a function (i.e. what f(x)=0). As such, when you have something like you have, you need to put it in that form first. So, sin(x) =x^2 then f(x):=sinxx2=0. You can now proceed. \[x_{n+1}=x_n\frac{f(x_n)}{f'(x_n)} \rightarrow x_{n+1}=x_n\frac{\sin x_n  x_n^2}{\cos x_n 2x_n}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So,\[x_1=1\frac{\sin(1)(1)^2}{\cos(1)2(1)} \approx 0.891395995\]and this number becomes your second input, and you keep going (technically, forever).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[x_2=0.891395995\frac{\sin (0.891395995)(0.891395995)^2}{\cos(0.891395995)2(0.891395995)}\]\[\approx 0.876984844\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Mathematica spits a terminating output of about 0.8767262153950624.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The other solution is x=0.
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