Exam 2: Limits and the Derivative

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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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Graph the function. -Graph the function. -

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Use point-by-point plotting to sketch the graph of the equation. -Use point-by-point plotting to sketch the graph of the equation. -

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Solve the problem. -U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) Solve the problem. -U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x)   980. How many families were there in 2002? 980. How many families were there in 2002?

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Solve the problem. -The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: per day: Solve the problem. -The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: per day:   The average cost per unit at The average cost per unit at a production level of players per day is per day is   (A) Find the rational function   (B) Graph the average cost function on a graphing utility for Graph the average cost function on a graphing utility for 10   (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)? The average cost per unit at The average cost per unit at a production level of players per day is per day is Solve the problem. -The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: per day:   The average cost per unit at The average cost per unit at a production level of players per day is per day is   (A) Find the rational function   (B) Graph the average cost function on a graphing utility for Graph the average cost function on a graphing utility for 10   (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)? (A) Find the rational function Solve the problem. -The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: per day:   The average cost per unit at The average cost per unit at a production level of players per day is per day is   (A) Find the rational function   (B) Graph the average cost function on a graphing utility for Graph the average cost function on a graphing utility for 10   (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)? (B) Graph the average cost function on a graphing utility for Graph the average cost function on a graphing utility for 10 Solve the problem. -The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: per day:   The average cost per unit at The average cost per unit at a production level of players per day is per day is   (A) Find the rational function   (B) Graph the average cost function on a graphing utility for Graph the average cost function on a graphing utility for 10   (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)? (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)?

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Graph by converting to exponential form first. -Graph by converting to exponential form first. -

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For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. -y = (x + 10)(x + 6)(x + 6)

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Solve the problem. -A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays According to the equation Solve the problem. -A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays According to the equation   )). )).

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Determine the domain of the function. -f(x) = Determine the domain of the function. -f(x) =

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Solve the problem. -In North America, coyotes are one of the few species with an expanding range. The future population of coyotes in a region of Mississippi valley can be modeled by the equation P = 59 + 12 · ln(18t + 1), where t is time in Years. Use the equation to determine when the population will reach 170. (Round your answer to the nearest Tenth year.)

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

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Provide an appropriate response. -Let T be the set of teachers at a high school and let S be the set of students enrolled at that school. Determine which of the following correspondences define a function. Explain. (A) A student corresponds to the teacher if the student is enrolled in the teacher's class. (B) A student corresponds to every teacher of the school.

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Provide an appropriate response. -The following graph represents the result of applying a sequence of transformations to the graph of a basic function. Identify the basic function and describe the transformation(s). Write the equation for the given graph. Provide an appropriate response. -The following graph represents the result of applying a sequence of transformations to the graph of a basic function. Identify the basic function and describe the transformation(s). Write the equation for the given graph.

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Determine whether the graph is the graph of a function. -Determine whether the graph is the graph of a function. -

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Determine whether the relation represents a function. If it is a function, state the domain and range. -{(-3, 10), (-2, 5), (0, 1), (2, 5), (4, 17)}

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

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Solve the problem. -Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 · ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth.

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Determine whether the function is linear, constant, or neither -Determine whether the function is linear, constant, or neither -

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Solve for x to two decimal places (using a calculator). -Solve for x to two decimal places (using a calculator). -

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For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -For the given function, find each of the following: (A) Intercepts (B) Vertex (C) Maximum or minimum (D) Range -

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