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Calculus 1: Newton Raphson Method

Use Newton's method for approximating roots of functions to approximate 0.99\sqrt{0.99}

Use the Newton Raphson method to approximate the real zero close to x=1x = 1 until two successive approximations differ by less than 0.005 for the following function

f(x)=2x23f(x) = 2x^2 - 3

Starting with an initial value x1=1x_1 = 1, perform 2 iterations of Newton's Method on f(x)=x3x1f(x) = x^3 - x - 1 to approximate the root.

Use Newton's Method to approximate the solution to the following equation

cos(x)=x5\cos{(x)} = \frac{x}{5}

Use Newton's Method to approximate a solution to 2cos(x)=3x2\cos{(x)} = 3x (Let x0=π6x_0 = \frac{\pi}{6} and find x2x_2)