Calculus Questions
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![dw dt For the given functions a express as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate w 6ye Inz x In 1 y tant z 1 1 dw at the given value of t dt by dw dt](https://media.kunduz.com/media/sug-question-candidate/20230626012332161260-4709559_FAgkLET.jpg?w=256)
Calculus
Differentiationdw dt For the given functions a express as a function of t both by using the Chain Rule and by expressing w in terms of t and differentiating directly with respect to t Then b evaluate w 6ye Inz x In 1 y tant z 1 1 dw at the given value of t dt by dw dt
![40Write a 40 Write your answer as a fraction or a whole or](https://media.kunduz.com/media/sug-question-candidate/20230424210913400804-4426144_Nxjnlsx.jpg?w=256)
![A fence must be built to enclose a rectangular area of 5000 ft2 Fencing material costs 1 per foot for the two sides facing north and south and 2 per foot for the other two sides Fin the cost of the least expensive fence The cost of the least expensive fence is](https://media.kunduz.com/media/sug-question-candidate/20230328210223454383-5422331_pAFmywe.jpg?w=256)
Calculus
Application of derivativesA fence must be built to enclose a rectangular area of 5000 ft2 Fencing material costs 1 per foot for the two sides facing north and south and 2 per foot for the other two sides Fin the cost of the least expensive fence The cost of the least expensive fence is
![A fence must be built to enclose a rectangular area of 5000 ft Fencing material costs 3 per foot for the two sides facing north and south and 6 per foot for the other two sides Find the cost of the least expensive fence The cost of the least expensive fence is Simplify your answer](https://media.kunduz.com/media/sug-question-candidate/20230327211351626119-5422331_g2nqwqN.jpg?w=256)
Calculus
Application of derivativesA fence must be built to enclose a rectangular area of 5000 ft Fencing material costs 3 per foot for the two sides facing north and south and 6 per foot for the other two sides Find the cost of the least expensive fence The cost of the least expensive fence is Simplify your answer
![A yeast culture is growing at the rate of W t 0 5e0 1t grams per hour If the starting culture weighs 5 grams what I will be the weight of the culture W t after t hours After 3 hours The weight of the culture after t hours will be W t](https://media.kunduz.com/media/sug-question-candidate/20230324211803786325-4364004_lE4YKyv.jpg?w=256)
Calculus
Differential equationsA yeast culture is growing at the rate of W t 0 5e0 1t grams per hour If the starting culture weighs 5 grams what I will be the weight of the culture W t after t hours After 3 hours The weight of the culture after t hours will be W t
![5 Verify that f and g are inverses f x x 7 g x 2x 14](https://media.kunduz.com/media/sug-question-candidate/20230322212053123830-5066220_gsn3W9p.jpg?w=256)
![Find the slope of the graph of the function at the given point Use the derivative feature of a graphing utility to confirm your results Function Point 0 0 f 0 8 sin 0 0 f 0](https://media.kunduz.com/media/sug-question-candidate/20230212213058394576-3392053_gv0Odnc.jpg?w=256)
Calculus
Indefinite IntegrationFind the slope of the graph of the function at the given point Use the derivative feature of a graphing utility to confirm your results Function Point 0 0 f 0 8 sin 0 0 f 0
![3 85 8 190 9 230](https://media.kunduz.com/media/sug-question-candidate/20230211211825865070-4558640_WMNxmay.jpg?w=256)
![A baseball diamond has the shape of a square with sides 90 feet long see figure A player running from second base to third base at a speed of 27 feet per second is 24 feet from third base At what rate in ft sec is player s distance from home plate changing Round your answer to two decimal places 3rd ft sec Home](https://media.kunduz.com/media/sug-question-candidate/20230208210207692510-3392053_Joq8CAm.jpg?w=256)
Calculus
Application of derivativesA baseball diamond has the shape of a square with sides 90 feet long see figure A player running from second base to third base at a speed of 27 feet per second is 24 feet from third base At what rate in ft sec is player s distance from home plate changing Round your answer to two decimal places 3rd ft sec Home
![y sin In 5x 2x Different](https://media.kunduz.com/media/sug-question-candidate/20240205101041924310-6121497.jpg?w=256)
![uestion z 6 5 4 3 2 1 3 y 4 5 46 3 6 Write an equation for the function graphed above](https://media.kunduz.com/media/sug-question-candidate/20240204234350123796-6566804.jpg?w=256)
Calculus
Limits & Continuityuestion z 6 5 4 3 2 1 3 y 4 5 46 3 6 Write an equation for the function graphed above
![Problem 3 Find the arc length of the graph of x e e from y 1 to y 1](https://media.kunduz.com/media/sug-question-candidate/20240205060639484260-6051355.jpg?w=256)
![Problem 2 Find the arc length of the graph of y from x 1 to x 3](https://media.kunduz.com/media/sug-question-candidate/20240205051046050060-6051355.jpg?w=256)
![Compute the following derivative using the method of your choi cos x5 sin 5x dx cos x5 sin 5x](https://media.kunduz.com/media/sug-question-candidate/20240205044304315385-5066220.jpg?w=256)
Calculus
Definite IntegralsCompute the following derivative using the method of your choi cos x5 sin 5x dx cos x5 sin 5x
![Find the arc length of the curve below on the given interval y In x x 1 for 1 x 65 Hint Integrate with respect to y The length of the curve is Simplify your answer](https://media.kunduz.com/media/sug-question-candidate/20240205044748630612-5066220.jpg?w=256)
Calculus
Definite IntegralsFind the arc length of the curve below on the given interval y In x x 1 for 1 x 65 Hint Integrate with respect to y The length of the curve is Simplify your answer
![Use a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule lim 1 3h h 0 Complete the table below Round to four decimal places as needed h 10 1 10 2 1 h 10 10 4 1 3h h h 10 1 2 10 10 10 4 3 1 1 3h](https://media.kunduz.com/media/sug-question-candidate/20240205044919816515-5066220.jpg?w=256)
Calculus
Application of derivativesUse a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule lim 1 3h h 0 Complete the table below Round to four decimal places as needed h 10 1 10 2 1 h 10 10 4 1 3h h h 10 1 2 10 10 10 4 3 1 1 3h
![Use a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule 17 1 X lim X 0 Complete the table below Do not round until the final answer Then round to six decimal places as needed 17 1 17 X 10 1 10 2 10 3 X h 10 1 10 2 10 3 X](https://media.kunduz.com/media/sug-question-candidate/20240205044951717152-5066220.jpg?w=256)
Calculus
Limits & ContinuityUse a calculator to make a table to approximate the following limit Confirm your result with l H pital s Rule 17 1 X lim X 0 Complete the table below Do not round until the final answer Then round to six decimal places as needed 17 1 17 X 10 1 10 2 10 3 X h 10 1 10 2 10 3 X
![Use the inverse relations between In x and e exp x and the properties of In x to prove the following properties a exp 0 1 b exp x y exp x exp y c exp x exp xy y rational a How can exp 0 be calculated Choose the correct answer below OA Find In exp 0 B Calculate exp 0 as the product of a constant and 0 c Find a value a for which In a 0 and substitute In a for 0 D Calculate the limit of exp x as x approaches 0 X S dt Recall that Inx X dt For what value is Type an exac answer X S dt 0](https://media.kunduz.com/media/sug-question-candidate/20240205045046151856-5066220.jpg?w=256)
Calculus
Definite IntegralsUse the inverse relations between In x and e exp x and the properties of In x to prove the following properties a exp 0 1 b exp x y exp x exp y c exp x exp xy y rational a How can exp 0 be calculated Choose the correct answer below OA Find In exp 0 B Calculate exp 0 as the product of a constant and 0 c Find a value a for which In a 0 and substitute In a for 0 D Calculate the limit of exp x as x approaches 0 X S dt Recall that Inx X dt For what value is Type an exac answer X S dt 0
![Find the volume of the solid generated when R shaded region is revolved about the given line 1 x y 1 x 1 about y 1 The volume of the solid obtained by revolving the region about 1 i 5x](https://media.kunduz.com/media/sug-question-candidate/20240205035246166434-5066220.jpg?w=256)
Calculus
Definite IntegralsFind the volume of the solid generated when R shaded region is revolved about the given line 1 x y 1 x 1 about y 1 The volume of the solid obtained by revolving the region about 1 i 5x
![Determine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d 2 2Inx 1 e The area under the curve y and above the x axis on the interval 1 e is 1 a Choose the correct answer below OA The statement is false because In 35 In 5 In 7 OB The statement is true For x 0 and y 0 In xy Inx In y by the Product Rule of Logarithms OC The statement is false because In 5 In 7 In 5 7 OD The statement is true For x 0 and y 0 In xy Inx In y by the Quotient Rule of Logarithms](https://media.kunduz.com/media/sug-question-candidate/20240205045006726509-5066220.jpg?w=256)
Calculus
Vector CalculusDetermine whether the following statements are true and give an explanation or counterexample Assume x 0 and y 0 a In xy Inx Iny b In 0 1 c In x y Inx Iny d 2 2Inx 1 e The area under the curve y and above the x axis on the interval 1 e is 1 a Choose the correct answer below OA The statement is false because In 35 In 5 In 7 OB The statement is true For x 0 and y 0 In xy Inx In y by the Product Rule of Logarithms OC The statement is false because In 5 In 7 In 5 7 OD The statement is true For x 0 and y 0 In xy Inx In y by the Quotient Rule of Logarithms
![Compute the following derivative using the method of your choice d cos x4 sin x dx d cos x4 sin x](https://media.kunduz.com/media/sug-question-candidate/20240205042634696672-5066220.jpg?w=256)
Calculus
DifferentiationCompute the following derivative using the method of your choice d cos x4 sin x dx d cos x4 sin x
![Determine the following indefinite integral Check your work by differentiation S5 dr dr](https://media.kunduz.com/media/sug-question-candidate/20240205042346579954-5066220.jpg?w=256)
Calculus
Definite IntegralsDetermine the following indefinite integral Check your work by differentiation S5 dr dr
![Evaluate the following integral Ax dx](https://media.kunduz.com/media/sug-question-candidate/20240205042938256535-5066220.jpg?w=256)
![Find the derivative of the function g x 5x 13x 3 et g x 5x 3x](https://media.kunduz.com/media/sug-question-candidate/20240205030841862577-6246774.jpg?w=256)
![Show all necessary work in your solutions Problem 1 Find the arc length of the graph of y x 2 3 2 from x 0 to x](https://media.kunduz.com/media/sug-question-candidate/20240205015851997984-6051355.jpg?w=256)
Calculus
Limits & ContinuityShow all necessary work in your solutions Problem 1 Find the arc length of the graph of y x 2 3 2 from x 0 to x
![Find the derivative of the function g x](https://media.kunduz.com/media/sug-question-candidate/20240205020646915849-6246774.jpg?w=256)
![Find the value of T S 2 esin a cos q dq 1 C 2](https://media.kunduz.com/media/sug-question-candidate/20240205020731716534-6246774.jpg?w=256)
![ind a formula for the inverse of the function z f x In 3x](https://media.kunduz.com/media/sug-question-candidate/20240205020542153646-6246774.jpg?w=256)
![ind the derivative of the function x g x 5x 3x](https://media.kunduz.com/media/sug-question-candidate/20240205020600714429-6246774.jpg?w=256)
![Construct a table of values to find the value of the limit from both sides for lim x 2 x 8 2 x](https://media.kunduz.com/media/sug-question-candidate/20240205014522125318-6560637.jpg?w=256)
Calculus
Limits & ContinuityConstruct a table of values to find the value of the limit from both sides for lim x 2 x 8 2 x
![Evaluate the following limits a b NOTE If needed enter INF for o and INF for o HINT Look at where the exponential fuction is going in the f 4 lim 200 ex 7 4 lim 2 0 e 7](https://media.kunduz.com/media/sug-question-candidate/20240205020629774668-6246774.jpg?w=256)
Calculus
Limits & ContinuityEvaluate the following limits a b NOTE If needed enter INF for o and INF for o HINT Look at where the exponential fuction is going in the f 4 lim 200 ex 7 4 lim 2 0 e 7
![Find the following integral Note that you can check your answer by differentiation S 6e4 3 3 dy](https://media.kunduz.com/media/sug-question-candidate/20240204232748217113-6246774.jpg?w=256)
Calculus
Indefinite IntegrationFind the following integral Note that you can check your answer by differentiation S 6e4 3 3 dy
![Find the following integral Note that you can check your answer by differentiatio S 6e4 y Vy dy](https://media.kunduz.com/media/sug-question-candidate/20240204225257117566-6246774.jpg?w=256)
Calculus
DifferentiationFind the following integral Note that you can check your answer by differentiatio S 6e4 y Vy dy
![Find the value of S 2 esin a cos q dq 2](https://media.kunduz.com/media/sug-question-candidate/20240204225237639338-6246774.jpg?w=256)
![Find the following integral Note that you can check your answer by differentiation S 7 e2z dx](https://media.kunduz.com/media/sug-question-candidate/20240204225219319665-6246774.jpg?w=256)
Calculus
Definite IntegralsFind the following integral Note that you can check your answer by differentiation S 7 e2z dx
![f x](https://media.kunduz.com/media/sug-question-candidate/20240204225144238144-6246774.jpg?w=256)
![et dy dz 5x y e C](https://media.kunduz.com/media/sug-question-candidate/20240204225158278061-6246774.jpg?w=256)
![Find the derivative of the function f x below f x ln 15 e 9 f x](https://media.kunduz.com/media/sug-question-candidate/20240204223227011213-6246774.jpg?w=256)
![The expression e7 9 6 can be written as ef a where f x is a function of x Find f x f x](https://media.kunduz.com/media/sug-question-candidate/20240204223050128810-6246774.jpg?w=256)
Calculus
Limits & ContinuityThe expression e7 9 6 can be written as ef a where f x is a function of x Find f x f x
![Solve each equation for A Solve In 11x 1 5 for x 0 B Solve e 8 1 3 for x x 3](https://media.kunduz.com/media/sug-question-candidate/20240204223118845759-6246774.jpg?w=256)
Calculus
Application of derivativesSolve each equation for A Solve In 11x 1 5 for x 0 B Solve e 8 1 3 for x x 3
![The expression e 8 52 can be written as ef 2 where f a is a function of x Find f x f x 0](https://media.kunduz.com/media/sug-question-candidate/20240204223029847446-6246774.jpg?w=256)
Calculus
Application of derivativesThe expression e 8 52 can be written as ef 2 where f a is a function of x Find f x f x 0
![Given functions Find 3x g x x 6 h x h x a hog x b State the domain in interval notation x](https://media.kunduz.com/media/sug-question-candidate/20240204142411487178-5863939.jpg?w=256)
Calculus
Application of derivativesGiven functions Find 3x g x x 6 h x h x a hog x b State the domain in interval notation x
![5 4 M 2 3 2 3 The minimum degree of the polynomial is 2 The minimum degree of the polynomial is 3 The minimum degree of the polynomial is 4 The minimum degree of the polynomial is 5 The minimum degree of the polynomial is 6 The leading coefficient is positive The leading coefficient is negative Based on the end behavior the polynomial is odd Based on the end behavior the polynomial is even](https://media.kunduz.com/media/sug-question-candidate/20240204144217067974-5863939.jpg?w=256)
Calculus
Application of derivatives5 4 M 2 3 2 3 The minimum degree of the polynomial is 2 The minimum degree of the polynomial is 3 The minimum degree of the polynomial is 4 The minimum degree of the polynomial is 5 The minimum degree of the polynomial is 6 The leading coefficient is positive The leading coefficient is negative Based on the end behavior the polynomial is odd Based on the end behavior the polynomial is even
![Determine the end behavior of f x 5x x 4 x 2 5 x 3 2 Ox y x y E](https://media.kunduz.com/media/sug-question-candidate/20240204135647326639-5863939.jpg?w=256)
![A fireworks mortar is launched straight upward from a pool deck platform 10 m off the ground at an initial velocity of 62 m sec The height of the mortar can be modeled by h t 4 9t 2 62t 10 where h t is the height in meters and t is the time in seconds after launch What is the maximum height Round to the nearest meter do not include units in your answer](https://media.kunduz.com/media/sug-question-candidate/20240204135843908711-5863939.jpg?w=256)
Calculus
DifferentiationA fireworks mortar is launched straight upward from a pool deck platform 10 m off the ground at an initial velocity of 62 m sec The height of the mortar can be modeled by h t 4 9t 2 62t 10 where h t is the height in meters and t is the time in seconds after launch What is the maximum height Round to the nearest meter do not include units in your answer
![Factor completely using synthetic division 3x 5x 4x 4 given that 2 is a root x intercept value Write the answer in linear factor form You must show work to receive credit](https://media.kunduz.com/media/sug-question-candidate/20240204141050729291-5863939.jpg?w=256)
Calculus
Definite IntegralsFactor completely using synthetic division 3x 5x 4x 4 given that 2 is a root x intercept value Write the answer in linear factor form You must show work to receive credit
![A salesperson makes a base salary of 1100 per month Once he reaches 38 000 in total sales he earns an additional 6 commission on the amount of sales over 38 000 Write a piecewise defined function to model the salesperson s total monthly salary in as a function of the amount in sales x](https://media.kunduz.com/media/sug-question-candidate/20240204140151574864-5863939.jpg?w=256)
Calculus
Limits & ContinuityA salesperson makes a base salary of 1100 per month Once he reaches 38 000 in total sales he earns an additional 6 commission on the amount of sales over 38 000 Write a piecewise defined function to model the salesperson s total monthly salary in as a function of the amount in sales x
![The monthly profit for a company that makes picture frames depends on the price per frame The company determines that the profit is approximated by P x 50x 80 000x 2500 where x is the price per frame and P x is the monthly profit based on that price Find the price that generates the maximum profit](https://media.kunduz.com/media/sug-question-candidate/20240204135050336800-5863939.jpg?w=256)
Calculus
Application of derivativesThe monthly profit for a company that makes picture frames depends on the price per frame The company determines that the profit is approximated by P x 50x 80 000x 2500 where x is the price per frame and P x is the monthly profit based on that price Find the price that generates the maximum profit
![Problem 5 Use the method of cylindrical shells to find the volume when the region bounded above by x y and x 2 y and below by the x axis and rotated around the x axis](https://media.kunduz.com/media/sug-question-candidate/20240204080550512136-6051355.jpg?w=256)
Calculus
Definite IntegralsProblem 5 Use the method of cylindrical shells to find the volume when the region bounded above by x y and x 2 y and below by the x axis and rotated around the x axis
![What is the angle measure 52 48 51 equivalent to in decimal degrees Enter your answer rounded to the nearest thousandth of a degree in the box](https://media.kunduz.com/media/sug-question-candidate/20240204072829025133-6563278.jpg?w=256)
Calculus
Limits & ContinuityWhat is the angle measure 52 48 51 equivalent to in decimal degrees Enter your answer rounded to the nearest thousandth of a degree in the box