1 c Kathryn Bollinger October 17 2010 Exam II Night Before Drill Fall 2010 Note This review is not intended to represent an actual exam These questions cover Sections 2 6 2 8 3 1 3 4 and 3 7 3 9 in Single Variable Calculus Concepts Contexts 4th Ed by Stewart Not every topic from each section is covered in this review Please also take a look at the previous Week in Reviews for more practice problems 3 1 Given y ln u2 8 and u 23x x find dy dx 2 The pulse rate in number of heartbeats per minute of a long distance runner t seconds after leaving the starting line is given by 300 0 5t2 2t 25 P t t 25 a Find P 120 and interpret your answer b Find P 120 and interpret your answer c Kathryn Bollinger October 17 2010 2 3 The position of a particle is given by the equation s t t3 18t2 81t where t is measured in seconds and s is measured in meters a What is the speed of the particle at time t 5 b When is the particle at rest c When is the particle moving forwards Backwards d What is the total distance traveled by the particle in the first 12 seconds e What is the acceleration of the particle at time t 5 c Kathryn Bollinger October 17 2010 3 f When is the particle speeding up Slowing down g What is the jerk of the particle at time t 4 Oil spilling from a tanker spreads in all directions so that the area polluted forms a circle The radius of the polluted area is increasing at a rate of 3 feet sec Determine how fast the polluted area is increasing after 20 seconds 4 c Kathryn Bollinger October 17 2010 5 Find the differential dy for y x 6 Consider the function f x 2 x 2x 1 a Find the linearization of f x at a 4 b Use the linearization found in a to estimate the value of 9 2 5 c Kathryn Bollinger October 17 2010 7 The annual cost tuition room and board of attending Math University is given for selected years in the table below Year t Cost C t 1990 7050 1992 8000 1994 9000 1996 9600 1998 10500 a Find the average rate of change in annual costs from 1992 to 1996 and interpret your answer b Estimate the rate of change in annual costs in 1992 by finding the average of two average rates of change Interpret your answer c Use a linear approximation to estimate the annual costs of attending Math University in 1993 6 c Kathryn Bollinger October 17 2010 8 Find the equations of the tangent and normal line to y 1 at x 1 1 x2 9 Fill in the blanks below f x 0 means that the graph of f x is and f x is f x is f x is f x 0 means that the graph of f x is and f x is f x 0 means that the graph of f x is and f x is and f x is f x 0 means that the graph of f x is x intercepts of f x appear as Local extrema of f x appear as in the graph of f x in the graph of f x 7 c Kathryn Bollinger October 17 2010 10 Given the graph of f x below sketch a graph of f x 2 2 2 2 2 2 2 2 c Kathryn Bollinger October 17 2010 11 Sketch the graph of a function that satisfies the following conditions x intercepts 1 0 and 2 0 Vertical Asymptotes at x 1 2 lim f x 0 x f 5 1 f 4 1 f x 0 on 4 1 2 and 2 f x 0 on 4 1 and 1 1 f x 0 on 6 and 1 2 f x 0 on 6 1 and 2 8 9 c Kathryn Bollinger October 17 2010 12 Use the graph below to answer the questions that follow 2 2 a If the given graph is that of f x where is f x 0 b If the given graph is that of f x where is f x decreasing c If the given graph is that of f x where is f x concave up d If the given graph is that of f x where is f x concave up 10 c Kathryn Bollinger October 17 2010 13 Use the limit definition of the derivative to find f x for f x 2x x 1 14 Find the first derivative of each of the following functions DO NOT SIMPLIFY 8 a f x log sin 5x xe 3x 9 xe5 11 c Kathryn Bollinger October 17 2010 b g x csc x5 tan x cos2 ln x c h x cot sec x2 10 x 2 7x 500
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