Page 1 of 4 Econo Calculus Course - SECton HocTro Show all your work and box all of your final answers. Question1 Find the derivative of the following using the chain rule: a) (8 points) y = tan (1 + VI) b) (8 points) g(x) - e-312Question2 (8 points) Find dy using implicit differentiation. ' y + In(x) = sin(y)Question4 Consider the following limit sin x lim a) (4 points) What indeterminate form is this limit? b) (6 points) Evaluate this limit using L'Hospital's RulePage 3 of 4 QuestionG Consider the function S(z) = 1 - 912 + 15z over the domain (-0o, co). Answer the following questions, and round, if needed, to 3 decimal places. a) (6 points) Find all critical valucs of f (I) b) (6 points) Using the First Derivative Test and the critical values you found in (a), state the intervals where f(z) is increasing and state the intervals where f(z) is decreasing. c) (3 points) State the coordinates for any local maximum or minimum of /(z). d) (4 points) Using ("(r), state the intervals where f(z) in concave down and state the intervals where J(I) is concave up, ") (3 points) State the coordinates for any Inflection points of S(x)Question8 A particle moves according to a law of motion s = 0.014 - 0.0463, where s is measured in feet, and t is measured in seconds for t 2 0 a) (6 points) Find the velocity at time t. b) (5 points) When (in seconds) is the particle at rest? c) (5 points) Find the acceleration after 2 seconds. Include units with your