Posted by Blair on Saturday, July 19, 2008 at 5:45pm.
Use Newton's method to approximate a root of the equation 5sin(x)=x as follows.
Let x1=2 be the initial approximation.
The second approximation x2 is:
and the third approximation x3 is:

Math  Damon, Saturday, July 19, 2008 at 6:11pm
5 sin x = x
let y = x  5 sin x, search for y = 0
dy/dx = y' = 1  5 cos x
Xn+1 = Xn + y(Xn)/y'at Xn
X1 = 2
y = 2  5 sin 2 = 2  4.54 = 2.54
y'=1  5 cos 2 = 3.08
X2 = 2 2.54/3.08 = 1.17
y = 1.17  5 sin 1.17 = 3.43
y' = 1  5 cos 1.17 = .951
X3 = 1.17 3.43/.951 = 4.77
This is unlikely to work the way you want because you are jumping from cycle to cycle of the original sine wave

Math  Blair, Saturday, July 19, 2008 at 6:52pm
The answers are wrong for this one.

Math  sign wrong  Damon, Saturday, July 19, 2008 at 7:47pm
sorry, sign wrong. I drew my picture wrong
5 sin x = x
let y = x  5 sin x, search for y = 0
dy/dx = y' = 1  5 cos x
Xn+1 = Xn  y(Xn)/y'at Xn
X1 = 2
y = 2  5 sin 2 = 2  4.54 = 2.54
y'=1  5 cos 2 = 3.08
X2 = 2 + 2.54/3.08 = 2.82
y = 2.82  5 sin 2.82 = 1.24
y' = 1  5 cos 2.82 = 5.74
X3 = 2.82 1.24/5.74 = 2.60

Math  Damon, Sunday, July 20, 2008 at 1:40pm
check my arithmetic carefully
Answer This Question
Related Questions
 calculus  Use Newton's method to approximate a root of the equation 3sin(x)=x ...
 calculus  Use Newton's method to approximate a root of the equation 3sin(x)=x ...
 Calculus  Use Newton's method to approximate a root of the equation (2 x^3 + 4 ...
 calculus  Use Newton's method to approximate a root of the equation 3sin(x)=x ...
 CALC  Use Newton's method to approximate a root of the equation x3+x+3=0 as ...
 calculus, math  Use Newton's method to approximate the value of (543)^(1/5) as ...
 Cal 1  Use Newton's method with the specified initial approximation x1 to find ...
 Calculus  Use Newton's method with the specified initial approximation x1 to ...
 CalculusNewton Method Approximation  Use Newton's method to approximate the ...
 Math  Use differential, (i.e. linear approximation), to approximate cube root ...
More Related Questions