Exam 2: Limits and the Derivative

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Provide an appropriate response. -For f(t) = 3 - 5t, find Provide an appropriate response. -For f(t) = 3 - 5t, find

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Graph the function using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. -Graph the function using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. -

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For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). -For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or  horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). -

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Solve the problem. -Under certain conditions, the power P, in watts per hour, generated by a windmill with winds blowing v miles per hour is given by Solve the problem. -Under certain conditions, the power P, in watts per hour, generated by a windmill with winds blowing v miles per hour is given by   . Find the power generated by 18 Find the power generated by 1-mph winds. . Find the power generated by 18 Find the power generated by 1-mph winds.

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Convert to an exponential equation. -Convert to an exponential equation. -

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Convert to a logarithmic equation. -Convert to a logarithmic equation. -

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Use the REGRESSION feature on a graphing calculator. -The average retail price in the Spring of 2000 for a used Camaro Z28 coupe depends on the age of the car as shown in the following table. Use the REGRESSION feature on a graphing calculator. -The average retail price in the Spring of 2000 for a used Camaro Z28 coupe depends on the age of the car as shown in the following table.   Find the quadratic model that best estimates this data. Round your answer to whole numbers. Find the quadratic model that best estimates this data. Round your answer to whole numbers.

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Solve the problem. -The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function Solve the problem. -The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function   where t i where t s the number of years since 1960. Estimate The of cases in the year 2010. where t i where t s the number of years since 1960. Estimate The of cases in the year 2010.

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Solve the problem. -Suppose that $2200 is invested at 3% interest, compounded semiannually. Find the function for the amount of money after t years.

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Solve the equation. -Solve for x: or x: Solve the equation. -Solve for x: or x:

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The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? -The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function  that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? -

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Provide an appropriate response. -Find the vertex and the maximum or minimum of the quadratic function on Provide an appropriate response. -Find the vertex and the maximum or minimum of the quadratic function on   by fir by first writing f in standard form. State the range of f and find the intercepts of f . by fir by first writing f in standard form. State the range of f and find the intercepts of f .

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The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? -The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function  that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? -

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Solve the problem. -The average weight of a particular species of frog is given Solve the problem. -The average weight of a particular species of frog is given   where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be Obtained from one of the six basic functions:   . (ii) Sketch a graph of Function w using part (i) as an aid.  where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be Obtained from one of the six basic functions: Solve the problem. -The average weight of a particular species of frog is given   where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be Obtained from one of the six basic functions:   . (ii) Sketch a graph of Function w using part (i) as an aid.  . (ii) Sketch a graph of Function w using part (i) as an aid. Solve the problem. -The average weight of a particular species of frog is given   where x is length (with legs stretched out) in meters and w(x) is weight in grams. (i) Describe how the graph of function w can be Obtained from one of the six basic functions:   . (ii) Sketch a graph of Function w using part (i) as an aid.

(Multiple Choice)
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For the rational function below (i) Find any intercepts for the graph; (ii) Find any vertical and horizontal asymptotes for the graph; (iii) Sketch any asymptotes as dashed lines. Then sketch a graph of f. -For the rational function below (i) Find any intercepts for the graph; (ii) Find any vertical and horizontal asymptotes for  the graph; (iii) Sketch any asymptotes as dashed lines. Then sketch a graph of f. -

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For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. -For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. -

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Solve the problem. -In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x) Represents the total profit for producing x widgets. Given x widgets. Given Solve the problem. -In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference P(x) = R(x) - C(x) Represents the total profit for producing x widgets. Given x widgets. Given   a and C(x) = 3x + 13, find P(100). a and C(x) = 3x + 13, find P(100).

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Use a calculator to evaluate the expression. Round the result to five decimal places. -Use a calculator to evaluate the expression. Round the result to five decimal places. -

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Give the domain and range of the function. -Give the domain and range of the function. -

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Find the equations of any vertical asymptotes. -Find the equations of any vertical asymptotes. -

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