Non-Linear EquationDate: 2/13/96 at 19:58:38 From: Budi Rachman Subject: Non-Linear Equation Can you give me a detailed solution for non-linear equations like this: 5x^2 + log(x) = 0 x = ? Thanks for your solution. Date: 7/29/96 at 16:32:17 From: Doctor Jerry Subject: Re: Non-Linear Equation Equations similar to this equation can't be solved in what is called closed form. They must be solved numerically, with an algorithm. There are several algorithms, some of which depend upon calculus. I'll give you some results from applying Newton's method, which depends upon calculus. If this is not appropriate, please ask again and I'll talk about the bisection method. Let f(x) = 5x^2+log(x). I assume log means natural logarithm. If you graph f you'll see that it crosses the x-axis near 0.5. The first guess at the zero c of f(x) will be x1=0.5. The next guess is x2 = x1-f(x1)/f'(x1) = 0.42045... For f(x) = 5x^2+log(x), the derivative function f' is f'(x)=10x+1/x. The next guess is x3 = x2-f(x2)/f'(x2) = 0.417797... The calculations continue in this pattern and converge quite rapidly to the zero c, which is approximately 0.417795. -Doctor Jerry, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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