Application of derivatives Questions and Answers
![Verify that each equation is an identity 37 sin x cos x sin 2x 1 39 tan 8k tan 8k tan 4k 2 tan 4k rample 3 38 sec 2x 40 sin 2x 2 tan x 1 tan x](https://media.kunduz.com/media/sug-question-candidate/20230215023512326952-4412862.jpg?w=256)
Calculus
Application of derivativesVerify that each equation is an identity 37 sin x cos x sin 2x 1 39 tan 8k tan 8k tan 4k 2 tan 4k rample 3 38 sec 2x 40 sin 2x 2 tan x 1 tan x
![Find the length of the following two dimensional curve r t 10 cos t 10 sin t for Osts The length of the curve is Type an exact answer using as needed](https://media.kunduz.com/media/sug-question-candidate/20230215023430158079-4345941.jpg?w=256)
Calculus
Application of derivativesFind the length of the following two dimensional curve r t 10 cos t 10 sin t for Osts The length of the curve is Type an exact answer using as needed
![For the following trajectory find the speed associated with the trajectory and then find the length of the trajectory on the given interval r t 4t t3 6t for Ost 4](https://media.kunduz.com/media/sug-question-candidate/20230215023342748539-4345941.jpg?w=256)
Calculus
Application of derivativesFor the following trajectory find the speed associated with the trajectory and then find the length of the trajectory on the given interval r t 4t t3 6t for Ost 4
![3 y 3 x 2x 4x 1 Avg Ava rate Avg rate between x 1 and x 41 A la](https://media.kunduz.com/media/sug-question-candidate/20230215020853184457-4742344.jpg?w=256)
![Consider the following trajectory of a moving object Find the tangential and normal components of the acceleration r t 11 cost 11 sint 24t a N T Type exact answers using radicals as needed](https://media.kunduz.com/media/sug-question-candidate/20230215013733530783-4345941.jpg?w=256)
Calculus
Application of derivativesConsider the following trajectory of a moving object Find the tangential and normal components of the acceleration r t 11 cost 11 sint 24t a N T Type exact answers using radicals as needed
![If f x f x f 5 4 sin x 2 cos x then](https://media.kunduz.com/media/sug-question-candidate/20230215014340390609-4565383.jpg?w=256)
![Use the alternative curvature formula x K r t 4 21 t 0 axv v to find the curvature of the following parameterized curve](https://media.kunduz.com/media/sug-question-candidate/20230215013305667069-4345941.jpg?w=256)
Calculus
Application of derivativesUse the alternative curvature formula x K r t 4 21 t 0 axv v to find the curvature of the following parameterized curve
![43 Draw a diagram and find the remaining part of the right triangle If b 48 A 36 a OA 51 B 35 C 66 D 29](https://media.kunduz.com/media/sug-question-candidate/20230215013506428517-4107770.jpg?w=256)
Calculus
Application of derivatives43 Draw a diagram and find the remaining part of the right triangle If b 48 A 36 a OA 51 B 35 C 66 D 29
![Find the unit tangent vector T and the principal unit normal vector N for the following parameterized curve Verify that T N 1 and T N 0 r t T 2 31 6](https://media.kunduz.com/media/sug-question-candidate/20230215013327265511-4345941.jpg?w=256)
Calculus
Application of derivativesFind the unit tangent vector T and the principal unit normal vector N for the following parameterized curve Verify that T N 1 and T N 0 r t T 2 31 6
![31 sin 8 48 cos 20 What is the second step to finde A 8 48 28 90 B 28 0 48 90 C 8 48 20 180 O D 28 8 48 180](https://media.kunduz.com/media/sug-question-candidate/20230215013219724363-4107770.jpg?w=256)
Calculus
Application of derivatives31 sin 8 48 cos 20 What is the second step to finde A 8 48 28 90 B 28 0 48 90 C 8 48 20 180 O D 28 8 48 180
![35 Draw and label a right triangle using the given sides then solve for the unknown side and write the trigonometric functions of angles A and B if a 5 and c 7 cos A OA OB 75 C 7 2 6 C 2 6 7 5](https://media.kunduz.com/media/sug-question-candidate/20230215013315007328-4107770.jpg?w=256)
Calculus
Application of derivatives35 Draw and label a right triangle using the given sides then solve for the unknown side and write the trigonometric functions of angles A and B if a 5 and c 7 cos A OA OB 75 C 7 2 6 C 2 6 7 5
![Find the unit tangent vector T and the curvature x for the following parameterized curve r t 7 cost 7 sint 7t Choose the correct answer for the unit tangent vector of r t 14 4 OA T t B T t OC T t K OD T t 14 4 1 VIA 1 4 sint 14 14 sin t 4 14 14 4 sin t sint cost 14 4 cost 14 2 cost 4 4 cost 2 4 2 4 2 4](https://media.kunduz.com/media/sug-question-candidate/20230215013243825856-4345941.jpg?w=256)
Calculus
Application of derivativesFind the unit tangent vector T and the curvature x for the following parameterized curve r t 7 cost 7 sint 7t Choose the correct answer for the unit tangent vector of r t 14 4 OA T t B T t OC T t K OD T t 14 4 1 VIA 1 4 sint 14 14 sin t 4 14 14 4 sin t sint cost 14 4 cost 14 2 cost 4 4 cost 2 4 2 4 2 4
![32 sin 8 48 cos 28 8 A 132 OB 14 O C 44 O D 42](https://media.kunduz.com/media/sug-question-candidate/20230215013236265174-4107770.jpg?w=256)
![26 sec 246 OA 1 095 OB 2 459 O C 1 095 D 2 459](https://media.kunduz.com/media/sug-question-candidate/20230215013109026371-4107770.jpg?w=256)
![Graph the following function Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima f x 4x Use the graphing tool to graph the function Click to enlarge graph Determine on which interval s f x is increasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB There is no interval on which the function f x is increasing Determine on which interval s f x is decreasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is decreasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB There is no interval on which the function f x is decreasing Determine the relative maxima or minima Select the correct choice below and if necessary fill in the answer box to complete your choice A The function has a relative minimum and the minimum value is OB The function has no relative minimum at x](https://media.kunduz.com/media/sug-question-candidate/20230215012211888590-5378010.jpg?w=256)
Calculus
Application of derivativesGraph the following function Estimate the intervals on which the function is increasing or decreasing and any relative maxima or minima f x 4x Use the graphing tool to graph the function Click to enlarge graph Determine on which interval s f x is increasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is increasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB There is no interval on which the function f x is increasing Determine on which interval s f x is decreasing Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function f is decreasing on the interval s Type your answer in interval notation Use a comma to separate answers as needed OB There is no interval on which the function f x is decreasing Determine the relative maxima or minima Select the correct choice below and if necessary fill in the answer box to complete your choice A The function has a relative minimum and the minimum value is OB The function has no relative minimum at x
![x cos y x y dx x dy 0 FINAL ANSWER y arctan ln x c1 x anx X](https://media.kunduz.com/media/sug-question-candidate/20230215005813354409-4438816.jpg?w=256)
![y x 2 dy 1 12 In 12 2 1 12 10 x 1 21 In x 1 In y arcsec c X c1 X Show the whole solution of the given problem and regarding with the final answer thats the one with below the equation which is 1 In and so on](https://media.kunduz.com/media/sug-question-candidate/20230215002016038597-4438816.jpg?w=256)
Calculus
Application of derivativesy x 2 dy 1 12 In 12 2 1 12 10 x 1 21 In x 1 In y arcsec c X c1 X Show the whole solution of the given problem and regarding with the final answer thats the one with below the equation which is 1 In and so on
![If f x 5x sin x cos x find f x f 3](https://media.kunduz.com/media/sug-question-candidate/20230215004336335363-4565383.jpg?w=256)
![If g x sin x then g x cos x g 2 0 42](https://media.kunduz.com/media/sug-question-candidate/20230215002108570016-4565383.jpg?w=256)
![Find the x values of all points where the function has any relative extrema Find the value s of any relative extrer f x x6 ex 8 Select the correct choice below and if necessary fill in any answer boxes within your choice OA There are no relative minima The function has a relative maximum of at x Use a comma to separate answers as needed Type exact answers in terms of e at x OB There are no relative maxima The function has a relative minimum of Use a comma to separate answers as needed Type exact answers in terms of e OC The function has a relative maximum of at x and a relative minimum of Use a comma to separate answers as needed Type exact answers in terms of e There are no relative extrema at x](https://media.kunduz.com/media/sug-question-candidate/20230214230309946350-5377348.jpg?w=256)
Calculus
Application of derivativesFind the x values of all points where the function has any relative extrema Find the value s of any relative extrer f x x6 ex 8 Select the correct choice below and if necessary fill in any answer boxes within your choice OA There are no relative minima The function has a relative maximum of at x Use a comma to separate answers as needed Type exact answers in terms of e at x OB There are no relative maxima The function has a relative minimum of Use a comma to separate answers as needed Type exact answers in terms of e OC The function has a relative maximum of at x and a relative minimum of Use a comma to separate answers as needed Type exact answers in terms of e There are no relative extrema at x
![Find the point if it exists at which the following plane and line intersect 4x 8y 6z 19 and x 10 7t y 9 9t z 3 4t Select the correct choice below and if necessary fill in any answer boxes to complete your choice A The point at which the line intersects the plane is Simplify your answers Type an ordered triple OB The line and the plane do not intersect](https://media.kunduz.com/media/sug-question-candidate/20230214232458310683-4345941.jpg?w=256)
Calculus
Application of derivativesFind the point if it exists at which the following plane and line intersect 4x 8y 6z 19 and x 10 7t y 9 9t z 3 4t Select the correct choice below and if necessary fill in any answer boxes to complete your choice A The point at which the line intersects the plane is Simplify your answers Type an ordered triple OB The line and the plane do not intersect
![15 Find the angle e to the nearest minute sin 8 0 1855 A 9 32 B 9 38 OC 9 39 D 9 31](https://media.kunduz.com/media/sug-question-candidate/20230214221459752184-4107770.jpg?w=256)
Calculus
Application of derivatives15 Find the angle e to the nearest minute sin 8 0 1855 A 9 32 B 9 38 OC 9 39 D 9 31
![Given the following number as an approximate measurement 49 5 feet What is the range of values for the actual value OA 49 0 to 50 0 OB 49 45 to 49 55 OC 49 49 to 49 51 D 49 4 to 49 6](https://media.kunduz.com/media/sug-question-candidate/20230214221012478047-4107770.jpg?w=256)
Calculus
Application of derivativesGiven the following number as an approximate measurement 49 5 feet What is the range of values for the actual value OA 49 0 to 50 0 OB 49 45 to 49 55 OC 49 49 to 49 51 D 49 4 to 49 6
![3 Perform the indicated operation and give each result with the proper number of significant digits 4 7 2 65 A 2 05 B 2 1 C 2 15 D 2 0](https://media.kunduz.com/media/sug-question-candidate/20230214221304167714-4107770.jpg?w=256)
Calculus
Application of derivatives3 Perform the indicated operation and give each result with the proper number of significant digits 4 7 2 65 A 2 05 B 2 1 C 2 15 D 2 0
![5 Round off 4 465 to one significant digit A 0 OB 5 OC 4 OD 3](https://media.kunduz.com/media/sug-question-candidate/20230214221200017710-4107770.jpg?w=256)
![3 Round off 4 465 to three significant digits A 4 45 B 4 50 C 4 46 D 4 47](https://media.kunduz.com/media/sug-question-candidate/20230214221058522260-4107770.jpg?w=256)
Calculus
Application of derivatives3 Round off 4 465 to three significant digits A 4 45 B 4 50 C 4 46 D 4 47
![for the angle whose terminal side passes through the point p 5 4](https://media.kunduz.com/media/sug-question-candidate/20230214215807980534-5351479.jpg?w=256)
![stion factors determine the amount of simple interest ean all that apply Number of bank accounts Time Interest rate](https://media.kunduz.com/media/sug-question-candidate/20230214211413443114-5352990.jpg?w=256)
Calculus
Application of derivativesstion factors determine the amount of simple interest ean all that apply Number of bank accounts Time Interest rate
![Find parametric equations that describe the circular path of the following object Assume x y denotes the position of the object relative to the origin at the center of the circle Use the units of time given in the description A go cart moves clockwise with constant speed around a circular track of radius 200 m completing one lap in 1 8 min Assume the center of the track is at the origin and that the go cart starts at 200 0 What are the parametric equations x t and y t Type exact answers using as needed](https://media.kunduz.com/media/sug-question-candidate/20230214194824034385-4345941.jpg?w=256)
Calculus
Application of derivativesFind parametric equations that describe the circular path of the following object Assume x y denotes the position of the object relative to the origin at the center of the circle Use the units of time given in the description A go cart moves clockwise with constant speed around a circular track of radius 200 m completing one lap in 1 8 min Assume the center of the track is at the origin and that the go cart starts at 200 0 What are the parametric equations x t and y t Type exact answers using as needed
![2 1 f x x 5x 7 2 f x 24 3 f x x 11x 6 4 f x x 3x 5 f x x 3x 1 Note 1 2 x x 41](https://media.kunduz.com/media/sug-question-candidate/20230214195605376564-4646611.jpg?w=256)
Calculus
Application of derivatives2 1 f x x 5x 7 2 f x 24 3 f x x 11x 6 4 f x x 3x 5 f x x 3x 1 Note 1 2 x x 41
![Consider the following parametric equations x t 2 y 4 t 0sts 16 a Eliminate the parameter to obtain an equation in x and y b Describe the curve and indicate the positive orientation](https://media.kunduz.com/media/sug-question-candidate/20230214194506590184-4345941.jpg?w=256)
Calculus
Application of derivativesConsider the following parametric equations x t 2 y 4 t 0sts 16 a Eliminate the parameter to obtain an equation in x and y b Describe the curve and indicate the positive orientation
![A regular Pentagon with sides that are 20m long is shown What is the approximate Area of the Pentagon](https://media.kunduz.com/media/sug-question-candidate/20230214193658729654-5216799.jpg?w=256)
Calculus
Application of derivativesA regular Pentagon with sides that are 20m long is shown What is the approximate Area of the Pentagon
![e interest is compounded more than once per year which rate is higher the ose the correct answer below A The stated rate is higher B The effective rate and the stated rate are the same C There is not enough information to decide D The effective rate is higher](https://media.kunduz.com/media/sug-question-candidate/20230214192554661376-5352990.jpg?w=256)
Calculus
Application of derivativese interest is compounded more than once per year which rate is higher the ose the correct answer below A The stated rate is higher B The effective rate and the stated rate are the same C There is not enough information to decide D The effective rate is higher
![the present value the amount that should be invested now to accumulate the followi Dounded as indicated 9000 at 9 compounded quarterly for 9 years present value is ot round until the final answer Then round to the nearest cent as needed](https://media.kunduz.com/media/sug-question-candidate/20230214192719883714-5352990.jpg?w=256)
Calculus
Application of derivativesthe present value the amount that should be invested now to accumulate the followi Dounded as indicated 9000 at 9 compounded quarterly for 9 years present value is ot round until the final answer Then round to the nearest cent as needed
![Question 13 5 2 3 ect all that apply at factors determine the amount of interest eamed on a fixed prin ount A Interest rate B Number of compounding periods C Frequency of periodic payments D None of the above EO](https://media.kunduz.com/media/sug-question-candidate/20230214192546262321-5352990.jpg?w=256)
Calculus
Application of derivativesQuestion 13 5 2 3 ect all that apply at factors determine the amount of interest eamed on a fixed prin ount A Interest rate B Number of compounding periods C Frequency of periodic payments D None of the above EO
![passes through 2 2 perpendicular to y 5x 8 CHALLENGE Find the value of n so that the line perpendicular to the line with equation 2y 4 6x 8 passes through the points at n 4 and 2 8](https://media.kunduz.com/media/sug-question-candidate/20230214184603149431-5376953.jpg?w=256)
Calculus
Application of derivativespasses through 2 2 perpendicular to y 5x 8 CHALLENGE Find the value of n so that the line perpendicular to the line with equation 2y 4 6x 8 passes through the points at n 4 and 2 8
![ptions Let x x 1 2 A 2 27 A 2 3 27 7 2 7 7 2 a sinh 2 4 12 f x x sin y f y dy Then a b is equal to 0 cos x xe IR be](https://media.kunduz.com/media/sug-question-candidate/20230214153634608850-5376953.jpg?w=256)
Calculus
Application of derivativesptions Let x x 1 2 A 2 27 A 2 3 27 7 2 7 7 2 a sinh 2 4 12 f x x sin y f y dy Then a b is equal to 0 cos x xe IR be
![ODD function Question 3 25 points A function f x is an EVEN function If f 4 2 which other point lies on the graph of g x 4 2 O 4 2 0 4 2 2 4](https://media.kunduz.com/media/sug-question-candidate/20230214171454647557-4083857.jpg?w=256)
Calculus
Application of derivativesODD function Question 3 25 points A function f x is an EVEN function If f 4 2 which other point lies on the graph of g x 4 2 O 4 2 0 4 2 2 4
![The definition of the derivative of a function is f x h f x f x lim h 0 h Write but do not attempt to compute the following derivatives I If f x 2 sin x f x lim h 0 II If f x ex tan x f x lim h 0 X](https://media.kunduz.com/media/sug-question-candidate/20230214150141110199-5376634.jpg?w=256)
Calculus
Application of derivativesThe definition of the derivative of a function is f x h f x f x lim h 0 h Write but do not attempt to compute the following derivatives I If f x 2 sin x f x lim h 0 II If f x ex tan x f x lim h 0 X
![What is the area of the largest equilateral triangle that can be cut from a circular piece of material 50 centimeters in diameter](https://media.kunduz.com/media/sug-question-candidate/20230214141305035691-5117549.jpg?w=256)
Calculus
Application of derivativesWhat is the area of the largest equilateral triangle that can be cut from a circular piece of material 50 centimeters in diameter
![2 12 13 15 17 and E 13 Insert or to make the A E 3 Corto make the statement true E](https://media.kunduz.com/media/sug-question-candidate/20230214143212065634-5352990.jpg?w=256)
Calculus
Application of derivatives2 12 13 15 17 and E 13 Insert or to make the A E 3 Corto make the statement true E
![Find the minimum value of the function f x y x y xy subject to the constraint 2x y 1 0](https://media.kunduz.com/media/sug-question-candidate/20230214124109132206-5376633.jpg?w=256)
Calculus
Application of derivativesFind the minimum value of the function f x y x y xy subject to the constraint 2x y 1 0
![9 Find a general solution to the following difference equation Yn 2 2Yn 1 Yn 1 3 Answer y C C n n n](https://media.kunduz.com/media/sug-question-candidate/20230214094941380724-5376634.jpg?w=256)
Calculus
Application of derivatives9 Find a general solution to the following difference equation Yn 2 2Yn 1 Yn 1 3 Answer y C C n n n
![Consider the following function Function Factors f x 2 x 3 x 2 6 x 3 quad 2 x 1 x sqrt 3 a Verify the given factors of f x b Find the remaining factor s of f x Enter your answers as a comma s c Use your results to write the complete factorization of f x f x d List all real zeros of f Enter your answers as a comma separated list e Confirm your results by using a graphing utility to graph the function](https://media.kunduz.com/media/sug-question-candidate/20230214070622142648-5376667.jpg?w=256)
Calculus
Application of derivativesConsider the following function Function Factors f x 2 x 3 x 2 6 x 3 quad 2 x 1 x sqrt 3 a Verify the given factors of f x b Find the remaining factor s of f x Enter your answers as a comma s c Use your results to write the complete factorization of f x f x d List all real zeros of f Enter your answers as a comma separated list e Confirm your results by using a graphing utility to graph the function
![0 You have 208 feet of fence to make a rectangular garden What are the dimensions of the garden that will enclose the largest area Type a response](https://media.kunduz.com/media/sug-question-candidate/20230214064607376139-5007618.jpg?w=256)
Calculus
Application of derivatives0 You have 208 feet of fence to make a rectangular garden What are the dimensions of the garden that will enclose the largest area Type a response
![For each function in Problems 25 30 find the relative maxima relative minima and horizontal points of inflection then sketch the graph Check your graph with a graphing utility 25 y x x x 1](https://media.kunduz.com/media/sug-question-candidate/20230214063458624516-5376635.jpg?w=256)
Calculus
Application of derivativesFor each function in Problems 25 30 find the relative maxima relative minima and horizontal points of inflection then sketch the graph Check your graph with a graphing utility 25 y x x x 1
![35 Find the numbers at which the function f x x 2 if x 0 et 2 x if 0 x 1 if x 1 is discontinuous At which of these points is f continuous from the right from the left or neither Sketch the graph of f](https://media.kunduz.com/media/sug-question-candidate/20230214051813175612-3764988.jpg?w=256)
Calculus
Application of derivatives35 Find the numbers at which the function f x x 2 if x 0 et 2 x if 0 x 1 if x 1 is discontinuous At which of these points is f continuous from the right from the left or neither Sketch the graph of f
![he separable IVP x t dx dt 4 with initial condition z 0 6 has solution X](https://media.kunduz.com/media/sug-question-candidate/20230214045443611251-3392387.jpg?w=256)
Calculus
Application of derivativeshe separable IVP x t dx dt 4 with initial condition z 0 6 has solution X
![du e u 3t u 0 13 dt has solution u t](https://media.kunduz.com/media/sug-question-candidate/20230214045536650777-3392387.jpg?w=256)
![On the interval 0 0 this separable IVP dy 9 11x dx xy has solution y x y 1 3](https://media.kunduz.com/media/sug-question-candidate/20230214045524750521-3392387.jpg?w=256)
Calculus
Application of derivativesOn the interval 0 0 this separable IVP dy 9 11x dx xy has solution y x y 1 3