Approximate the zero(s) of the function. Use Newton's Method and continue the process until two successive approximations differ by less than 0.001. Then find the zero(s) using a graphing utility and compare the results. f(x) = 2x + sin(x) Newton's method: Graphing utility: X X =

Use Newton's method to find the positive root of the equation x2 –- 2 = 0 to five decimal points. %3D

At noon, the tide is at mid tide of 11 feet. At 6:00 pm, the tide is at low tide of 3 feet. At 6:00 am, the tide is at its high tide of 19 feet. It takes 24 hours for the tide to complete a full cycle. Determine a sinusoidal function that models the tide height h as a function of time t(in hours). Let t = 0 correspond to noon. - High tide Mid tide Low tide d

Tide height as a function of time resembles a sinusoidal function during the time between low and high tide. At one such location on another planet with water, the tide has a high of 12.7 feet at 2 am and then the next low is -0.8 feet at 11 am (9 hours later). Find a formula for a sinusoidal function H(t) that gives the height tt hours after midnight.

An object weighing W pounds is suspended from the ceiling by a steel spring. The weight is pulled downward (positive direction) from its equilibrium position and released (see figure). The resulting motion of the weight is described by the function y = e-t/8 cos(8t), where y is the distance in feet and t is the time in seconds (t > 0). 2 (a) Use a graphing utility to graph the function. y 1 12 2 y 7 5 3 Equilibrium -3- -5 AAAAA на As t increases, y →→ π WET t 1 ∞011 FE 4 8 8 y 20 15 10 5 -5 -10 -15 O-20 (b) Describe the behavior of the displacement function for increasing values of time t. K 4 KIN 2 KIN Л Зл 4 15~ 3л π 27 t t