Calculus Questions

a Determine the equation of the line that passes through A 2 5 and is parallel to the line with an equation of 3x 2y 5 b Determine the equation of the line perpendicular to the line 3 having equation y x 6 and passing through the point 4

Determine the values of x for which the function is continuous function is not continuous the reason If the determine a x 6x 15 b x 2 x 7x

Consider the following function v x Answer if x 2 6 4 x if x 2 Step 1 of 3 Identify the general shape and direction of the graph of this function on the interval o 2 776 X x

Use implicit differentiation to find dy dx x 3x y y 8

Find the derivative of y with respect to x y cos 7x 4

Answers parts a through e a Express the volume V of the box as a function of the length x of the side of the square cut from each corner V 225x 60x 4x Simplify your answer b What is the volume if a 2 inch square is cut out The volume is 242 cubic inches Simplify your answer c What is the volume if a 6 inch square is cut out The volume is 54 cubic inches Simplify your answer d Graph V V x For what value of x is V largest Choose the correct graph below an example Q Search K An open box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each comer and turning up the sides See the figure d Graph V V x For what value of x is V largest Choose the correct graph below OA Get more help Xmin 0 Xmax 7 5 Xscl 0 5 Ymin 0 Ymax 275 Yscl 25 For what value of x is V largest X EIN 5 inches B Xmin 0 Xmax 7 5 Xscl 0 5 Ymin 0 Ymax 275 Yscl 25 come OC Q Xmin 0 Xmax 7 5 Xscl 0 5 Ymin 0 Ymax 130 Yscl 10 OD Clear all Q Q 15 m XminEO Xmar 15 Od 0 Ymin 0 Ymax 275 Yad 25

Use Fleury s Algorithm to find an Euler circuit Write an Euler circuit starting at A CHE D A E C LL

Exploration 2 2 3 The P x Problem A concept Given integers a b and c such that 0 a b and given P x x x a x b 13 where P x is divisible by x c 1 Find a b and c 2 Is your solution unique Justify your answer 41 64 onl

Identify the even vertices and identify the odd vertices LIF Use a comma to separate answers as needed OA The only odd vertex is OB The odd vertices are G Use a comma to separate answers as needed B D OC There are no even vertices Identify the odd vertices Select the correct choice below and if necessary fill in the answer box to complete your choice Ea G

box with a square base is to be made from a square piece of cardboard 15 inches on a side by cutting out a square from each corner and turning up the sides See the figure Answers parts a through e a Express the volume V of the box as a function of the length x of the side of the square cut from each corner 3 V 225x 60x 4x Simplify your answer b What is the volume if a 2 inch square is cut out The volume is 60 cubic inches Simplify your answer 0 8 of 1

If 9000 is invested for t years at 8 interest compounded continuously the future value is given by S 900000 dollars Complete parts a through e a Graph this function for Osts 15 Choose the correct graph below OB AS 34 000 c Complete the following table t Year S 8 17 068 33 Round to the nearest whole number as needed AS Complete the following table t Year S 5 5 34 000 Q b Use the graph to estimate when the future value will be 20 000 Choose the correct answer below A 19 98 years B te 19 96 years VC 20 Type an integer or decimal rounded to two decimal places as needed AS 34 000 OC t 8 98 years o 5 OD 34 000 00 1

Find the center of mass of a thin triangular plate bounded by the y axis and the lines y x and y 2 xif 8 12x 2y 6 The plate s center of mass is located at Simplify your answer Type an ordered pair Use integers or fractions for any numbers in the expression

S V y 32 1 5 4 3 2 1 4 2 3 4 S 1 2 3 4 5 Complete an equation for the function graphed above Enter abs x for x

Let f x 3 x If g x is the graph of f x shifted up 4 units and right 4 units write a formula for g x g x Enter as sqrt x

Question 8 Sketch a graph of f x 2x 4 2 5 4 3 2 1 5 4 3 2 1 T Question Help 1 2 3 4 5 Clear All Draw Video 1 1 2 3 4 V 5

Let f x 3 x If g x is the graph of f x shifted down 5 units and right 2 units write a formula for g x g x

O Question 7 6 5 3 2 6 5 4 3 2 2 NO 3 75 5 6 1 2 3 4 5 S The graph above is a transformation of the function x Write an equation for the function graphed above Question Help Video Message instructor

4 The graph of a function g is shown on the ay plane on the interval 7 7 a A table of selected values is given for a different function h which has only one real zero 3 h x 5 2 2 7 0 3 2 0 13 20 VAN

Question 6 Describe a function g x in terms of f x if the graph of g is obtained by vertically stretching f by a factor of 4 then shifting the graph of f to the right 2 units and upward 7 units g x Af x B C where A B C

A survey approximates the number of Americans that are age 65 and older and projects that by the year 2050 approximately 82 4 million Americans will be at least 65 The bar graph shows the estimated number of Americans with projected figures for the year 2020 and beyond A graphing calculator screen displays an exponential function that models the U S population age 65 and over y in millions x years after 1899 Use this information to solve a d below Click the icon to view the bar graph a Explain why an exponential function was used to model the population data A An exponential function was used because exponential functions are always more accurate than linear functions OB An exponential function was used because the data in the bar graph is increasing more and more rapidly OC An exponential function was used because population is always modeled using exponential functions OD An exponential function was used because there are too many data points to use a linear function b Use the graphing calculator screen to express the model in function notation with numbers rounded to three decimal places f x 0 c According to the model in part b how many Americans age 65 and over were there in 2010 Use a graphing calculator million Type an integer or a decimal rounded to one decimal place as needed Does this rounded number overestimate or underestimate the 2010 population displayed by the bar graph By how much Choose the correct answer below and fill in the answer box to complete your choice Type an integer or decimal rounded to one decimal place as needed OA The rounded number overestimates the 2010 population by OB The rounded number underestimates the 2010 population by million million I d According to the model in part b how many Americans age 65 and over will there be in 2020 ExpReg y a b x a 3 500502606 b 1 022918115

An open box with a square base is to be made from a square piece of cardboard 9 inches on a side by cutting out a square from each corner and turning up the sides See the figure Answers parts a through e c What is the volume it a 3 inch square is cut out The volume is 27 cubic inches Simplify your answer d Graph V V x For what value of x is V largest Choose the correct graph below OA Q Q Xmin 0 Xmax 4 5 Xscl 0 5 Ymin 0 Ymax 60 Yerl 10 OB Xmin 0 Xmax 4 5 Xscl 0 5 Ymin 0 Ymax 60 Yerl 10 O C Q Xmin 0 Xmax 4 5 Xscl 0 5 Ymin Ymax 20 Yaels C O D a Q 2 Xmin 0 Xmax 45 Xsd 0

Next question For the following exercise write a formula for the function obtained when the graph is shifted as described f x g x Get a similar question You can retry this question below is shifted down 2 units and to the left 6 units 2 6 2 X Question Help VIDEO D Post to forum

Question 4 For the following exercise write a formula for the function obtained when the graph is shifted as described 1 is shifted down 3 units and to the left 8 units H Question Help VIDEO D Post to forum

Which scatter plot indicates a perfect negative correlation A D The graph shows a scatter plot with a perfect negative correlation D B B E C F

K Let P t be the population in millions of a certain city t years after 2015 and suppose that P t satisfies the differential equation P t 0 04P t P 0 7 a Use the differential equation to determine how fast the population is growing when it reaches 9 million people b Use the differential equation to determine the population size when it is growing at a rate of 800 000 people per year c Find a formula for P t a Choose the correct process to find how fast the population is growing when it reaches 9 million people OA Evaluate P t 0 04 9 OB Solve 9 0 04P t for P t OC Solve P 9 0 04P t for P t OD Evaluate P t 0 04P 9 C The population is growing at about million Type an integer or decimal rounded to two decimal places as needed b Choose the correct process to find the population size when it is growing at a rate of 800 000 people per year OA Evaluate P t 0 04P 0 8 OB Solve P 0 8 0 04P t for P t OC Solve 0 8 0 04P t for P t O D Evaluate P t 0 04 0 8 when it reaches 9 million people The population size is about million Type an integer or decimal rounded to two decimal places as needed when it is growing at a rate of 800 000 people per year

8 f 1 1 3 g t 1 Find pXr

8 A trough is 10 ft long and its ends have the shape of isos celes triangles that are 3 ft across at the top and have a height of 1 ft If the trough is being filled with water at a rate of 12 ft3 min how fast is the water level rising when the water is 6 inches deep

26 g u 2u 3u b C 28 y ae V 30 u 2 73 32 ye 1

Find an equation of the tangent line to the graph of f x ex where x 2 9 The equation of the tangent line is Type an equation Type your answer in slope intercept form Use integers or decimals for any numbers in the equation Round to two decimal places as needed

Question 7 Let f x 13x 12 x Question He

18 y x 20 f t t 1 t 22 y x x 1 24 y x 2 x

25 y 47 27 y ax bx c 1 13 29 v 1 31 z A Bey

Find the centroid of the region in the first quadrant bounded by the x axis the parabola y 8x and the line x y 6 The coordinates of the centroid are x y Simplify your answers Type an ordered pair Type simplified fractions

17 G x x 2et 19 F x x 5 21 g x x 23 y 1 x x 4x 3

Question 3 For the following exercise describe how the graph of the function is a transformation of the graph of the original function f y f x 6 8 Horizontal shift Vertical shift units Select an answer and unit Select an answer Question Help VIDEO Post to forum Submit

The velocity of a parachutist during free fall is f t 65 1 e 0 15t 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 8 seconds m sec b What is the approximate acceleration when t 0 m sec c Approximately when is the parachutist s velocity 50 m sec seconds d Approximately when is the acceleration 5 m sec seconds Ay 70 60 50 40 30 20 10 0 0 f 10 20 30

K The size of a certain insect population is given by P t 400e01t where t is measured in days a How many insects were present initially b Give a differential equation satisfied by P t c At what time will the population double d At what time will the population equal 2400 a There were insects b Choose the correct differential equation below OA P t 01P t OB P t 01e 01t OC P t In 01t OD P t e 01t c t days Round to one decimal place as needed d t days Round to one decimal place as needed

The table to the right shows teenage drug use in different countries Make a scatter plot for the given data Use the scatter plot to describe whether or not the variables appear to be related Make a scatter plot of the given data Choose the correct graph below O A 40 20 04 0 20 40 60 Marijuana 96 G OB 40 20 10 0 20 40 60 Marijuana Q Q OC 40 20 0 0 Country A B C D E F 20 40 60 Marijuana 96 Q Who Have Used Other Illegal Marijuana X 24 20 42 4 40 15 Drugs y 4 5 25 1 17 7 OD 40 20 0 Country G H 1 J K Who Have Used Other Illegal Drugs y 13 5 4 31 22 Marijuana X 23 6 6 50 34 0 20 40 60 Marijuana 96 Q

In an animal hospital 14 units of a certain medicine were injected into a dog After 45 minutes only 7 units remained in the dog Let f t be the amount of the medicine present after t minutes At any time the rate of change of f t is proportional to the value of f t Find the formula for f t The formula is f t Use integers or decimals for any numbers in the equation Round to three decimal places as needed

Find the coordinates of the relative extreme point of the given function and determine if the point is a relative maximum point or a relative minimum point f x ex 9x The coordinates of the relative extreme point are Type an ordered pair Type an exact answer Is the point a relative maximum point or a relative minimum point relative maximum point relative minimum point

Given f x 3x 4 and g x 2x 5 find f g x O A x 1 O B 5x 1 C 5x 1 O D 5x 9

Differentiate the following function f x e x 6 Choose the correct setup below to start differentiating the function OA 3x 6 x e d O B x 6 x e dx dx O C d dx OD dx d d x 6 6 e3x e6 dx 3x 6 x 6 dx dx d dx e x 6 3x 6 dx

Differentiate the function y In 2x 2x 9 y

f x 1 In x 5 What can f x 1 In x 5 OA In x 5 6 OB In x 5 be rewritten as C In x6 5 OD In x 5 1 Which derivative rule should be applied first d O A The chain rule f g x p h x h x p x h x p x h x h x OC The power rule if p x x for any number r then p x x 1 d OD The product rule p x h x p x h x h x p x B The quotient rule d p x dx h x

Differentiate the following function y x ex dy dx 11

f t 1 4 4 t 8

4 2 y x 5 17 1 4 r 3 V r 3 9

9 Y t 6t

3 4 V r 1 1 r 3

x r 8 1 2 4