Question

Use Newton's method to find the positive value of x which satisfies x = 1.1cos(x). Compute enough approximations so that your answer is within 0.05 of the exact answer. x = (Remember to calculate the trig functions in radian mode!)

Answer 1

To use Newton's method to find the positive value of x which satisfies x = 1.1cos(x), start with an initial guess and use the formula xn+1 = xn - f(xn)/f'(xn) to find successive approximations.

Step-by-step explanation:

To use Newton's method to find the positive value of x which satisfies x = 1.1cos(x), we will start with an initial guess and use the formula xn+1 = xn - f(xn)/f'(xn) to find successive approximations. Let's start with an initial guess of x0 = 1.

Step 1: Evaluate f(xn) = xn - 1.1cos(xn) and f'(xn) = 1 + 1.1sin(xn)

Step 2: Substitute the values of x0, f(x0), and f'(x0) into the formula to find x1.

Step 3: Repeat step 2 until the difference between two successive approximations is less than 0.05. The final approximation will be the positive value of x that satisfies the equation.