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Use a graphing utility to graph the function Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​ ​


A) ​ Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ Use a graphing utility to graph the function ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​If the total revenue function for a blender is ​If the total revenue function for a blender is ,determine how many units x must be sold to provide the maximum total revenue in dollars. ​ A) ​625 B) ​15,000 C) ​25 D) ​300 E) ​50 ,determine how many units x must be sold to provide the maximum total revenue in dollars. ​


A) ​625
B) ​15,000
C) ​25
D) ​300
E) ​50

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Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of ​ A) length 1.5; width 1.25 B) length 2; width 1 C) length 0.5; width 1.75 D) length 1; width 1.5 E) none of the above Find the dimensions of the rectangle of maximum area bounded by the x-axis and y-axis and the graph of ​ A) length 1.5; width 1.25 B) length 2; width 1 C) length 0.5; width 1.75 D) length 1; width 1.5 E) none of the above ​


A) length 1.5; width 1.25
B) length 2; width 1
C) length 0.5; width 1.75
D) length 1; width 1.5
E) none of the above

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When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​


A) ​ When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ , , When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ ,
B) ​ When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ , , When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ ,
C) ​ When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ , , When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ ,
D) ​ When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ , , When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ ,
E) ​​ When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ , , When the price of a glass of lemonade at a lemonade stand was $1.75,400 glasses were sold.When the price was lowered to $1.50,500 glasses were sold.Assume that the demand function is linear and that the marginal and fixed costs are $0.10 and $ 25,respectively.Find the marginal profit when 300 glasses of lemonade are sold and when 700 glasses of lemonade are sold. ​ A) ​ , B) ​ , C) ​ , D) ​ , E) ​​ ,

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​Use the properties of logarithms to write the expression as a single logarithm. ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Use the properties of logarithms to write the expression as a single logarithm. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​Find the third derivative of the function ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Find the third derivative of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​

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Sketch the graph of the function Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​ ? ​


A) ​ Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ Sketch the graph of the function ? ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes Confirm your results analytically.​ ​ ​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes ​ ​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes


A) ​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes
B) ​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes
C) ​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes
D) ​​ ​A function and its graph are given.Use the graph to find the horizontal asymptotes,if they exist,where Confirm your results analytically.​ ​ ​ ​ ​ A) ​ B) ​ C) ​ D) ​​ E) ​no horizontal asymptotes
E) ​no horizontal asymptotes

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​Analyze and sketch a graph of the function ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Analyze and sketch a graph of the function ​ A) ​ B) ​ C) ​ D) ​ E) ​

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Find Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0 for the equation Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0 by implicit differentiation and evaluate the derivative at the point Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0 ​


A) Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0
B) Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0
C) Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0
D) Find for the equation by implicit differentiation and evaluate the derivative at the point ​ A) B) C) D) E) 0
E) 0

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A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​ Find the derivative of the model. ​


A) ​ A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ A survey of high school seniors from a certain school district who took the SAT has determined that the mean score on the mathematics portion was 450 with a standard deviation of 11.5.By a normal probability density function the data can be modeled as Find the derivative of the model. ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​Write the equation of the line passing through the given pair of points. ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Write the equation of the line passing through the given pair of points. ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​For the given function,find the relative minima. ​ ​ ​For the given function,find the relative minima. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative minima ​


A) ​ ​For the given function,find the relative minima. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative minima
B) ​ ​For the given function,find the relative minima. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative minima
C) ​ ​For the given function,find the relative minima. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative minima
D) ​ ​For the given function,find the relative minima. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative minima
E) ​no relative minima

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​Find the x-values (if any) at which the function ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) is not continuous.Which of the discontinuities are removable? ​


A) ​no points of discontinuity
B) ​ ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (not removable) , ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (removable)
C) ​ ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (removable) , ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (not removable)
D) no points of continuity
E) ​​ ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (not removable) , ​Find the x-values (if any) at which the function is not continuous.Which of the discontinuities are removable? ​ A) ​no points of discontinuity B) ​ (not removable) , (removable) C) ​ (removable) , (not removable) D) no points of continuity E) ​​ (not removable) , (not removable) (not removable)

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​Find the derivative of the following function. ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
B) ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Find the derivative of the following function. ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​

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​Suppose that ​Suppose that and Find the following limit: ​ ​ A) ​13 B) ​24 C) ​2 D) ​-143 E) ​11 and ​Suppose that and Find the following limit: ​ ​ A) ​13 B) ​24 C) ​2 D) ​-143 E) ​11 Find the following limit: ​ ​Suppose that and Find the following limit: ​ ​ A) ​13 B) ​24 C) ​2 D) ​-143 E) ​11 ​


A) ​13
B) ​24
C) ​2
D) ​-143
E) ​11

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​Find all relative minima of the given function. ​ ​ ​Find all relative minima of the given function. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative maxima ​


A) ​ ​Find all relative minima of the given function. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative maxima
B) ​ ​Find all relative minima of the given function. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative maxima
C) ​ ​Find all relative minima of the given function. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative maxima
D) ​ ​Find all relative minima of the given function. ​ ​ ​ A) ​ B) ​ C) ​ D) ​ E) ​no relative maxima
E) ​no relative maxima

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​Write the equation of the line through ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​ that is perpendicular to ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​ ​


A) ​ ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​
B) ​ ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​
C) ​ ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​
D) ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​
E) ​ ​Write the equation of the line through that is perpendicular to ​ A) ​ B) ​ C) ​ D) E) ​

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What lump sum should be deposited in an account that will earn at an annual rate of 9%,compounded quarterly,to grow to $150,000 for retirement in 20 years? Round your answer to the nearest cent.


A) $147,330.10
B) $18,292.68
C) $53,571.43
D) $24,961.93
E) $25,294.49

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​Find ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​ ,if ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​


A) ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​ ​
B) ​ ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​
C) ​ ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​
D) ​ ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​
E) ​ ​Find ,if ​ A) ​ B) ​ C) ​ D) ​ E) ​

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