3) Solve the equation sin(x) = ln(x) x1 = f(x) = f'(x) = X≈

The equation 2^x = x^2 actually has three solutions: 2, 4, and a third solution which is a negative irrational number. Use Newton’s Method to find this number correct to 5decimal places, using ?$=−1. List each ?2, ?3, ...leading up to your final answer.

Explain why Newton’s method fails when applied to the equation cube root of x = 0 with any initial approximation  x1  not equal to 0 Illustrate your explanation with a sketch.

Use Newton's method to approximate a solution of the equation e-3* = -4x + 5, starting with the initial guess indicated. *₁ = -4 *₂ = -5.319 x3 = -5.383 The solution to the equation found by Newton's method is x = -5.383