Question

Use Newton's Method to find the two solutions of e x =6x to six significant figures. For this problem you will need to use the fact that the exponential equals its own derivative, i.e.,

dx / d e x =e x

Answer 1

To find the solutions of the equation e^x = 6x using Newton's Method, follow the steps: guess an initial value, use the tangent line formula to find the next value, repeat until desired accuracy, and the final values are the solutions accurate to six significant figures.

Step-by-step explanation:

To find the solutions of the equation ex = 6x using Newton's Method, we can follow these steps:

1. Start with an initial guess, let's say x0 = 1.
2. Use the equation of the tangent line to approximate the next value of x, which is given by the formula: xn+1 = xn - (f(xn) / f'(xn)), where f(x) is the given equation and f'(x) is its derivative. In this case, f(x) = ex - 6x and f'(x) = ex - 6.
3. Repeat step 2 until the desired level of accuracy or number of iterations is reached.
4. The two solutions, accurate to six significant figures, are the final values of x obtained from step 3.