Apply Newton's Method three times to determine an approximate value of the zero of f(x) = ex -5, starting with an initial guess of xo = 2. Express your approximation to five decimal pla Note: If your calculator cannot hold enough decimal places during your calculations, you will need to use Desmos, GeoGebra, or another similar graphing calculator with high precision. X3 =

During Ricardo noticed an ink stain with a diameter of about 3 cm on the front of his teacher’s shirt. He then noticed that there was a pen in the pocket and that the ink blot was continuing to spread across the front of the teacher’s shirt. He estimated that the diameter of the ink blot seemed to be growing by about 0.5 cm every 2 minutes. a) Write an equation for the RADIUS, r, of the ink stain, as a function of time, t. Assume that t = 0 represents the time that Ricardo first noticed the ink stain. b) Write an equation showing the AREA, A, of the ink stain as a function of the time t. (Hint: It might help to first write A as a function of r. ) c) Draw a graph of the function A(t) for 10 minutes. d) At what time is the area of the ink stain about 25 square centimeter? Show how you answer this question. (i.e. ”I found it using desmos” is not sufficient)

If you want to find the roots of the function f(x), Newtons method will always work.

Q1: Write a program to compute the following equation (Y=5x2 + 2), when the .input values greater than 5 Q2: Find the derivative and integral to the :following equation x4 + 213 - 3x2 + 5