Calculus Questions

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The velocity of a parachutist during free fall is f t 82 1 e 0 12t meters per second Answer the following questions using the graph Recall that acceleration is the derivative of velocity a What is the approximate velocity when t 4 seconds m sec C 80 70 60 50 40 30 20 10 0 0 fft fath 10 20 30 o

Find f x f x x 15 f x

Differentiate the following function f t

Find the point s on the graph of y x 168 ex where the tangent line is horizontal www Identify the point s on the graph of y x2 168 ex where the tangent line is horizontal 0 Type an ordered pair Type an exact answer Use a comma to separate answers as needed

Find the equation of the tangent line to the curve y et 1 8eX at What is the equation of the line tangent to the curve at 0 3 at 0 7 2

Identify the choice that best completes the statement or answers the question Question 3 714444 7 55567899 80112 87 Key 68 represents a flight that lasted 6 8 minutes Which of the following is the data set that would produce the stemplot dy A statistics student wins an aerial drone in a raffle The drone is advertised to have eight minutes of flight time on a single battery charge The student collected data to determine if the advertised time was accurate A stemplot shows the observed flight times in minutes O87 81 75 68 71 74 76 74 78 79 75 77 74 74 75 79 81 80 82 8 7 8 1 7 5 6 8 7 1747 6 747 8 7 9 7 5 7 7 7474 7 5 7 9 8 1 8 0 8 2 8 7 8 1 7 5 6 8 7 1 7 4 7 6 7 4 7 8 7 9 7 5 7 7 7 3 74 7 5 7 9 8 1 8 0 8 2 87 81 75 68 71 74 76 74 78 79 75 77 73 74 75 79 81 80 82 1 pts

Use a graphing utility to approximate the real solutions Round to two decimal places x 3x 3x 6x 1 0 Solution 1 Solution 2

10 5 10 5 5 5 10 For which values in the domain is this graph decreasing Give your answer in interval notation Assume the graph extends to finity in both directions

10 5 10 5 5 10 For which values in the domain is this graph increasing Give your answer in interval notation Assume the graph extends to finity in both directions Submit

stlon 8 Solve each equation for the variable Write only the number as your answer Problem A 9x180 B 6 4x 2 C 8x 7 31 D 6x 10 104 E 3 x 9 36 F 5 1 G 14 6x 4 H 6 5 Answer Correct X X X X X X X X V

Given the two points A 1 7 and B 3 15 Find the mid point s

X 2 Given that f x x 2x 10 find f 2

What is the solution set for the following inequality 2r 820 Use the buttons and boxes to create your answer ab a b a b Your Interval Notation Answer

X Answer the questions seen f x 2x 10 a What is the x intercept b What is the y intercept c Find f 3 Question a Answe

ab ab ab Question 2 as Write your question below What is the domain for the function f x x 1 Interval

VE bo x Solve the equation 13x 11 10 Show yo Round to one decimal place as needed Solution 1 Solu

22 X 3 12 2

27 What is the value of n if 8 2n 3 28 What is the value of a if 272 9a 29 If 3a 1 x and 3a 30 If 25b 1 x and 5b y express y in terms of x x and 5b y express x in terms of

Macmillan Lear Use the graphs of f dashed line and g solid line in the following figure a 2 1 3 2 1 0 1 2 f x 1 N 2 1 T 3 1 4 g x 5 6 7 X 8 Find the domain of the function f o g Give your answer as an interval in the form Use the symbol oo for infinity U for combining inte type of parenthesis depending on whether the interval is open or closed Enter if the in numbers in exact form Use symbolic notation and fractions where needed

If h 2 9 and h 2 3 find d h x dx X 13 6 X x 2 Ws Enhanced Feedback Please try again You have to use the Quotient Rule to solve this problem To apply the Qu d f x x a x f x

23 a lim x 4 x 5 x 4 b lim x 4 x 5 x 4 x 5 c lim x 4 x 4

21 44 Determining limits analytically Determine the following limits 21 a 1 lim x 2 x 2 1 x 2x 2 b lim 1 x 2x 2 c lim

A group of friends wanted to take a 10 day backpacking trip to Wyoming They checked the weather forecast for their destination s daily low temperatures The dotplot below shows the daily low temperatures in degrees Fahrenheit for their 10 day trip Delly Low Tempente What is the interpretation of the dot above 46 in the dotplot The dot above 46 represents the last day of the trip and about 70 of the days should be cooler than 41 degrees O The dot above 46 represents the warmest day of the trip and about 60 of the days should be cooler than 41 degrees O The dot above 46 represents the last day of the trip and about 60 of the days should be cooler than 41 degrees The dot above 46 represents the warmest day of the trip and about 70 of the days should be cooler than 41 degrees

sthenes estimated the circumference of the Earth as 250 000 stadia the length of an athletic stadium If we assume he used the most common length of stadia of his time his estimate of the circumference of the Earth would be 46 620 km Currently the accepted average circumference of the Earth is 40030 2 km Find the percentage error of Eratosthenes estimate of the circumference of the Earth a Calculate the actual and an approximate temperature in C using the standard formula and Tommaso s grandmother s rule b Calculate the percentage error of the approximate tempe vo

b Find the derivative by expanding the product first h z 5 2 2 22 5 a Use the product rule to find the derivative of the given function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is 2 2z 5 OB The derivative is 5 2 2 2z 5 OC The derivative is 5 2 2 2z 5 OD The derivative is 5 z 2 2z 5 OE The derivative is 5 2

b Find the derivative by multiplying the expressions first y 3 x 2 x a Use the Product Rule to find the derivative of the function Select the correct answer below and fill in the answer box es to complete your choice OA The derivative is 3 x 2 B The derivative is 3 x 2 2x x OC The derivative is 3 x 2 x D The derivative is b Multiply the expressions x x TULE 3 2 x 5 2 3 x 2 x 3x 2x 2 Simplify your answer Now take the derivative of the answer from the previous step and simplify the answer from part a Check to make sure that the two results are the same That is using either approach y

The temperature T of a person during an illness is given by T t a Find the rate of change of the temperature with respect to time b Find the temperature at t 1 hr c Find the rate of change of the temperature at t 1 hr 98 6 where T is the temperature in degrees Fahre 1 2 a Find the rate of change of the temperature with respect to time 5 1 2 2 T t b Find the temperature at t 1 hr T 1 F Round to two decimal places as needed

Find y 5 dy dx

The equ 6200 R v V can be used to determine the heart rate R of a person whose heart pumps 6200 milliliters mL of blood per minute and v milliliters of blood per beat Complete parts a through c below a Find the rate of change of heart rate with respect to v the output per beat R v 6200 b Find the heart rate at v 90 mL per beat The heart rate is beats min Round to two decimal places as needed STO Heart rate 100 100 Output per beat 200

If y 1 10 X dy find dx at x 2 The value of dy dx Simplify your answer at x 2 is

For the polynomial below 3 is a zero g x x 9x 24x 18 Express g x as a product of linear factors g x 0

f f x x find f 11 11 Type an exact answer

In t years the population of a certain city grows from 100 000 to a size P given by P t 100 000 400C dP a Find the growth rate dt b Find the population after 15 yr c Find the growth rate at t 15 d Explain the meaning of the answer to part c B

Question 24 Solve 8y2 10y 3 y Question Help Message instructor

The population P in thousands of a small city is given by the following function where t is time in years Answer parts a through c P t AP 50 40 30 20 10 0 0 600t 21 25 1 2 32 ti 56 78 9 10 11 12 a Find the growth rate The growth rate is

Previous Solve the given equation If there are more than one solution separate 75 44

25 4 Question 26 a b 25 40 answered Simplify 80x6y to the form a b Quectio

Multiply and simplify completely 3xy 10 Your answer will be in the form A B where A and B are expressions Enter your expressions for A and B in the boxes below A B 6x1026

Utility is a type of function that occurs in economics When a consumer receives x units of a certain product a certain amount of pleasure or utility U is derived The graph represents a typical utility function a Find the average rate of change of U as x changes from 0 to 1 from 1 to 2 from 2 to 3 from 3 to 4 b Why do the average rates of change decrease as x increases a The average rate of change of U as x changes from 0 to 1 is Type an integer or a decimal The average rate of change of U as x changes from 1 to 2 is Type an integer or a decimal The average rate of change of U as x changes from 2 to 3 is Type an integer or a decimal The average rate of change of U as x changes from 3 to 4 is Type an integer or a decimal b Why do the average rates of change decrease as x increases Utility pleasure units AU 150 100 50 2 102 3 128 1 64 1 1 4 149 2 3 Number of units of product OA The average rate of change is the ratio of the change in utility U divided by the change in number of units of product x While U is increasing as x increases the change in U is decreasing Therefore the average rates of change decrease as x increases Q Q Time Remaining 01 21 04 G OB The average rate of change is the ratio of the number of units of product x divided by the change in utility U While U is decreasing as x increases the change in U is increasing Therefore the average rates of change decrease as x increases OC The average rate of change is the ratio of the number of units of product x divided by the change in utilitv U While U is increasing as x increases the change in U is decreasing Therefore Next

The graph of a function f is shown 800 400 0 0 20 40 c Compute the following f 40 f 0 40 0 60 a Find the average rate of change of f on the interval 50 60 b Identify an interval on which the average rate of change of f is 0 O 20 40 O 0 80 O 0 60 O 10 40 O 10 50 X What does this value represent geometrically O the slope of the tangent line at 0 f 0 d Estimate the value of f 50 O the slope of the tangent line at 40 f 40 O the slope of the line segment from 0 f 0 to 40 f 40 O the slope of the tangent line at 20 f 20

Find an equation of the tangent line to the graph of y The tangent to the curve at the origin is y 0 2x 2 1 at the origin and at the point 1 1 www

K Graph the function and then find the specified limits If necessary state that the limit does not exist f x 3x find lim f x and lim f x x 0 X 2 use the graphing tool to graph the function Click to enlarge graph Find lim f x Select the correct choice below and if necessary fill in the answer box to complete x 0 your choice OA lim f x x 0 B The limit does not exist Find lim f x Select the correct choice below and if necessary fill in the answer box to X 2 complete your choice OA lim f x X 2 B The limit does not exist C 10 8 4 2 10 18 Ay 6 4 2 2 4 6 8 10 2

Question 11 For the function f x 4x 10 evaluate and simplify the difference quotient Question Help Video Message instructor

5t 98 6 where T is the temperature in degrees Fahrenheit at time t in hours 2 The temperature T of a person during an illness is given by T t a Find the rate of change of the temperature with respect to time b Find the temperature at t 1 hr c Find the rate of change of the temperature at t 1 hr a Find the rate of change of the temperature with respect to time T t AT 1 102 98 0

Question 6 If x x 2 g x x 3 and h x then f g h x

Question 8 Given f x Domain 1 x 4 V and g x 16 x 3 find the domain of f g x

Graph the function and then find the specified limits When necessary state that the limit does not exist 3x 10 for x 4 for x 4 F x OA X Find lim F x lim F x lim F x X 4 X 4 X 4 OA lim F x X 4 OB The limit does not exist OA OB Ay IM Find lim F x Select the correct choice below and if necessary fill in the answer box within your choice x 4 lim F x X 4 OB The limit does not exist O C Find lim F x Select the correct choice below and if necessary fill in the answer box within your choice X 4 Ay Q O D Q Time Remaining 01 23 11

a Graph the function f x 2x 9x 10 b Draw a tangent line to the graph at the point whose x coordinate is 3 O A b Choose the correct graph of the tangent line OA Ay Q OA f 3 Q Simplify your answer O B B There is no solution O B Ay Ay Q D c f x d Select the correct choice below and if necessary fill in the answer box to complete your choice O C O C Ay Q G O D O D Q Time Remaining 01 18 52 Next

6200 R v V can be used to determine the heart rate R of a person whose heart pumps 6200 milliliters mL of blood per minute and v milliliters of blood per beat Complete parts a through c below a Find the rate of change of heart rate with respect to v the output per beat R v b Find the heart rate at v 50 mL per beat The heart rate is beats min Round to two decimal places as needed c Find the rate of change at v 50 mL per beat The rate of change is beats min per mL Round to two decimal places as needed Heart rate 200 R v 100 100 Output per beat 200