Question

Use Newton's method to find the positive value of [Variable] which satisfies [Equation]. Compute enough approximations so that your answer is within 0.05 of the exact answer.

a) Iterative numerical method
b) Root-finding algorithm
c) Matrix inversion technique
d) Linear interpolation

Answer 1

Newton's method is an iterative numerical method that can be used as a root-finding algorithm to find the positive value of a variable that satisfies an equation. It involves choosing an initial estimate, calculating function values and slopes, and iteratively updating the estimate until the desired accuracy is achieved. This method is more accurate than the graphical technique due to its use of calculus.

Step-by-step explanation:

Newton's method is an iterative numerical method that can be used as a root-finding algorithm to find the positive value of a variable that satisfies an equation. Here are the steps to use Newton's method:

1. Choose an initial estimate for the value of the variable.
2. Plug the initial estimate into the equation to compute a function value.
3. Calculate the slope of the function at the initial estimate.
4. Use the formula xn+1 = xn - f(xn)/f'(xn) to update the estimate, where f(x) is the function and f'(x) is its derivative.
5. Repeat steps 2-4 until the estimate is within the desired accuracy.

Newton's method is potentially more accurate than the graphical technique because it uses calculus to find the slope of the function, which can help converge to the solution faster and with more precision.