Big 10 Unit 4 Review Instructions: In the box below are the numbers 0-9. Complete the following and cross off the number for each answer. If you complete all problems correctly, you will cross off each number exactly once! 0 1 2 3 4 5 6 7 8 9 Use the graph of f(x) and the table for the differentiable function g(x) below for all questions. 1 f (x) 4 3 2 1 2 1 2 3 4 5 6 0 1 -1 g(2) g'(x) 2 -1 3 0 -1 5 3 4. 7 5 9 -3 9(2.x + 1) - 5 1. Evaluate lim 2-9 2. Approximate the value of g(6) using the tangent line to g(x) at x = 5. 3. If the position of a particle moving along the x-axis is given as æ(t) = 2 – 4t +5, at what time t> 0 is the particle at rest? 4. If the side length of a cube is increasing at a rate of inch per second when the cube has a side length of 2 inches, at what rate is the volume of the cube increasing with respect to time when the side length is 2 inches? 5. Suppose a particle is moving along the x-axis with velocity v(t) = 2t2 – 6t + 5 where t > 0. What is the only integer time, t > 0, where the particle is slowing down? Big 10 Unit 4 Review 4. 3 2 1 6 . 1 2 3 4. 5 0 1 3 5 7 g(x) 2 3 0 3 5 g'() -1 -3 -2 4 9 6. A water tank is filling up with water at a rate of w(t) = ? - t. What is the rate of change of the rate at which the water is filling up in the tank at t = 5 seconds? 7. Given that f'(1) = 4, approximate the value of f(3) using the tangent line to f(x) at x = 1. How much of an overapproximation is your estimate of the true value of f(3)? 8. If the velocity of a particle is given as v(t) = ecos(t), find the acceleration of the particle at t=7 9. The area of an irregular shape, A, with given side length S is given by the equation A = $2 - 2S. When the side length S is 3 feet, it is known that the side length is increasing at a rate of 2 feet per second. What is the rate of change of the area of the shape with respect to time at the instant S = 3 feet? 2 + 10 10. Evaluate lim 2-0 sin(2.c)