Estimate Roots In this investigation you will explore a technique for estimating the solution to an equation (e.g. when finding a root). Use Newton's method to provide a solution to ONLY ONE of the following: b) Find the solution to the following function to 2 decimal places. Start with an initial guess of x = 0 2x - 1 = sin x / 5 marks Newton's Method of Finding Roots To estimate a solution, say x = r to the equation f(x) = 0, following the steps below repeatedly. 1. Begin with an initial guess x₁ (It would be great to pick a guess that is close to the solution.) f(x) 2. Calculate (a better guess) x₂ = x₁ f(x₂) 3. If X is known then X =x- n+1 12 72 4. If x and x agree to k decimal places, then x approximates the root 1 up 11 n+1 to k decimal places and f(x) = 0. Watch the following clips if the above steps are still not clear to you. https://youtu.be/cOmAk82cr9M https://youtu.be/ER5B_YBFMJO 15 marks