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Exam 1: Functions, graphs, and Limits

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Exam 1: Functions, graphs, and Limits427 Questionsadd course
Exam 2: Differentiation84 Questionsadd course
Exam 3: Applications of the Derivative122 Questionsadd course
Exam 4: Exponential and Logarithmic Functions122 Questionsadd course
Exam 5: Integration and Its Applications88 Questionsadd course
Exam 6: Techniques of Integration46 Questionsadd course
Exam 7: Functions of Several Variables113 Questionsadd course
Exam 8: Trigonometric Functions60 Questionsadd course
Exam 9: Probability and Calculus36 Questionsadd course
Exam 10: Series and Taylor Polynomials104 Questionsadd course
Exam 11: Differential Equations77 Questionsadd course
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​A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 22 feet.Round yours answers to two decimal places. ​A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see figure).Find the dimensions of a Norman window of maximum area if the total perimeter is 22 feet.Round yours answers to two decimal places. ​ ​

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Question 21

Sketch the graph of the function Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. ​ using any extrema,intercepts,symmetry,and asymptotes. ​

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Question 22

​Determine whether the given function is continuous.If it is not,identify where it is discontinuous. ​ ​Determine whether the given function is continuous.If it is not,identify where it is discontinuous. ​ ​​ ​​

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Question 23

Consider a certificate of deposit that pays 14% (annual percentage rate)on an initial deposit of $3,000.The balance after 14 years is Consider a certificate of deposit that pays 14% (annual percentage rate)on an initial deposit of $3,000.The balance after 14 years is Estimate ,where x is the length of the compounding period (in years).Round your answer to the nearest hundredth. ​​ Estimate Consider a certificate of deposit that pays 14% (annual percentage rate)on an initial deposit of $3,000.The balance after 14 years is Estimate ,where x is the length of the compounding period (in years).Round your answer to the nearest hundredth. ​​ ,where x is the length of the compounding period (in years).Round your answer to the nearest hundredth. ​​

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Question 24

Use the properties of exponents to simplify the expression Use the properties of exponents to simplify the expression ​ ​

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Question 25

Use the Midpoint Formula repeatedly to find the three points that divide the segment joining Use the Midpoint Formula repeatedly to find the three points that divide the segment joining and into four equal parts. ​ and Use the Midpoint Formula repeatedly to find the three points that divide the segment joining and into four equal parts. ​ into four equal parts. ​

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Question 26

Find the length of each side of the right triangle from the following figure. Find the length of each side of the right triangle from the following figure. ​ ​

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Question 27

​Find the rate of change of x with respect to p. ​ ​Find the rate of change of x with respect to p. ​ , ​ , ​Find the rate of change of x with respect to p. ​ , ​ ​

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Question 28

​Write the equation and graph the line that passes through the given point and has the slope indicated. ​Write the equation and graph the line that passes through the given point and has the slope indicated. with 0 slope ​ with 0 slope ​

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Question 29

Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line. ​ Point: Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line. ​ Point: Line: ​ Line: Write an equation of the line that passes through the point (i)parallel to the given line,and (ii)perpendicular to the given line. ​ Point: Line: ​ ​

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Question 30

​Find any horizontal asymptotes for the given function. ​ ​ ​Find any horizontal asymptotes for the given function. ​ ​ ​ ​

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Question 31

​Write the equation of the line tangent to the graph of ​Write the equation of the line tangent to the graph of ​ ​

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Question 32

Write the general form of the equation of the circle with endpoints of a diameter at Write the general form of the equation of the circle with endpoints of a diameter at ​ ​ Write the general form of the equation of the circle with endpoints of a diameter at ​ ​ Write the general form of the equation of the circle with endpoints of a diameter at ​ ​ ​ ​

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Question 33

​Medication.The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by ​Medication.The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by Find the t-value at which x is maximum.Round your answer to two decimal places. ​ ​Medication.The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by Find the t-value at which x is maximum.Round your answer to two decimal places. ​ Find the t-value at which x is maximum.Round your answer to two decimal places. ​

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Question 34

​Find the derivative of the function. ​ ​ ​Find the derivative of the function. ​ ​ ​ ​

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Question 35

​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by ​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when ​ where t is the time (in hours).Find the rate of change of the population when ​A population of bacteria is introduced into a culture.The number of bacteria P can be modeled by where t is the time (in hours).Find the rate of change of the population when ​ ​

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Question 36

​Which of the following is the correct graph of ​Which of the following is the correct graph of ? ​ ? ​

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Question 37

​If ​If ,find ​ ,find ​If ,find ​ ​

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Question 38

The cost C (in dollars)of producing x units of a product is given by The cost C (in dollars)of producing x units of a product is given by Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. ​ Find the additional cost when the production increases from 9 to 10.Round your answer to two decimal places. ​

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Question 39

​Find any critical numbers of the function ​Find any critical numbers of the function ​. ​ ​. ​

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Question 40
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