Calculus Questions

5 The elevation of a path is given by f x x 5x 30 measured in feet where measures horizontal distances in miles Draw a graph of the elevation function and find its average value for 0 x 4

3 The rate of growth of a fish population was modeled by the equation 0 61 G t 60 000e 1 5e06 where t is measured in years since 2000 and G in kilograms per year If the biomass was 25 000 kg in the year 2000 what is the predicted biomass for the year 20303

2 Evaluate x x 1dx the integral

A company producing computer components has established that on the average a new employee can assemble N t components per day after t days of on the job training as indicated in the following table a new employee s productivity usually increases with time on the job up to a leveling off point UNA 96 t N t 3 15 12 0 12 132 20 53 5 40 70 B 96 60 78 TER The number of units is approximately Round to the nearest integer as needed 132 80 83 Q Q G SEEX 100 86 OC 96 3 5 12 120 87 132 Q OD 96 3 12 132 B Use the regression equation and a numerical integration routine on a graphing calculator to approximate the number of units assembled by a new employee during the first 100 days on the job CO

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the fth day The company s marginal cost per day is given by C C where C t is the total accumulated cost in dollars on the fth day R t 90e R 0 0 C t 90 0 8t C O 0 a Find the total profit P T from t 0 to t 10 the first 10 days P T R T C T S R C 0 at dt The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed

Find the area between the curve and the x axis over the indicated interval y 121 x 11 11 The area under the curve is Simplify your answer

what the shaded area represents Choose the correct answer below OA The total number of miles traveled in t hours OB The total number of hours it takes to travel t miles OC The aver miles per hour in t hours OD The average number of miles traveled in t hours Velocity in miles per hour Time ir

A company finds that the marginal profit in dollars per foot from drilling a well that is x feet deep is given by P x 3 x Find the profit when a well 250 ft deep is drilled Set up the integral for the total profit for a well that is 250 feet deep P 250 JOdx 0 The total profit is Round to two decimal places as needed

The total accumulated costs C t and revenues R t in thousands of dollars respectively for a photocopying machine satisfy 1 C t 1 and 76 R t 5t e t where t is the time in years Find the useful life of the machine to the nearest year What is the total profit accumulated during the useful life of the machine The useful life of the machine is year s Round to the nearest year as needed

Show that fand g are inverse functions algebraically graphically and numerically f x 5x 6 g x x 6 X x20 a algebraically f g x W g f x 9 b graphically y 15 X 10 f 3 15 10 g 3 J x c numerically 10 12 14 10 12 14 x 15 10 15 10 g 16 20 10 12 10 12 14

Consider the following functions f x g x 2 X Show that f and g are inverse functions algebraically f g x f g f x g 2 2 Use a graphing utility to graph fand g in the same viewing window Describe the relationship between the gi The graph of f is the translation of the graph of g relative to the line y x The graphs of fand g are the same as the graph of y x The graphs are the same The graph of f is the reflection of the graph of g in the line y x

A company producing electric motors has established that on the average a new employee can assemble N t components per day after t days of on the job training as shown in the table below a new employee s productivity increases continuously with time on the job Use left and right sums to estimate the area under the graph of N t from t 0 to t 60 Use three subintervals of equal length for each Calculate an error bound for each estimate t N t 0 11 250 Using left sums the area is Simplify your answer 40 66 60 76 80 100 120 81 85 86 GELEB

a Calculate the definite integral f x dx by referring to the figure on the right with the indicated areas a b Ay Area A 1 204 Area B 2 308 Area C 3 079 Area D 1 687

Sketch the function 3 p x x x 2x The end behavior of the gunction is on the right and on the left

Question Answer Attempt 1 out of 2 The function y f x is graphed below What is the average rate of change of the function f z on the interval 6 2 10 8 6 4 2 100 80 60 40 20 20 40 60 80 100 6 8 10 Submit Answer Watch Video x Show Examples

Careers G google translate G Member Login US YouTube to Mp3 C CCBubble Knee Len estion answer Attempt 1 out of 2 10 8 6 e function y f x is graphed below What is the average rate of change of the function f x on the interval 1 x 0 4 2 100 So 60 0 20 20 40 y A 60 80 100 2 6 8 O Watch Video 10 All Bookmarks Show Examples

Rotate the axes to eliminate the xy term in the equation Then write the equation in standard form Use xp for x and yp for y in your answer Rotate the coordinate axes through an angle with 0 0 2 9x 24xy 16y 80x 60y 0 x 4y X Check which variable s should be in your answer Sketch the graph of the resulting equation showing both sets of axes y SP 2 4 2

A W30x99 hot rolled structural steel wide flange shape is used as a simply supported beam on a span of 32 ft as shown below The beam supports a superimposed uniformly distributed load of 4 0 kips ft in addition to its own weight Calculate the maximum bending stress A 4 kips ft 32 W30 x 99 fin 27 X I Sect A A X

Question 1 20 points 1 Find the areas bounded by the indicated curves y x y 2 x x 0 x 0

F x sindt sindt F 0

Find the area bounded by y x 27x 54 the x axis and the first coordinates of the relative maximum and minimu values of the function The area is 0 Simplify your answer GETTE

Suppose the temperature in degrees Celsius over a 9 hour period is given by T t 1 6t 32 a Find the average temperature b Find the minimum temperature c Find the maximum temperature a The average temperature is 32 degrees Type an integer or a decimal Round to one decimal place as needed b The minimum temperature is degrees Type an exact answer in simplified form

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated rever in dollars on the fth day The company s marginal cost per day is given by C t where C t is the total accumulated cost in dollars on the fth day R t 130e R 0 0 C t 130 0 1t C 0 0 a Find the total profit P T from t 0 to t 10 the first 10 days P T R T C T S R t C t dt www The total profit is Round to the nearest cent as needed

36 A company is constructing an open top square based rectangular metal tank that will have a volume of 61 ft3 What dimensions yield the minimum surface area Round to the nearest tenth if necessary A 5 ft x 5 ft x 2 5 ft C 5 7 ft x 5 7 ft x 1 9 ft B 11 ft x 11 ft 0 5 ft D 3 9 ft x 3 9 ft 3 9 ft 36

Find the area of the region bounded by the graphs of the given equations y x y x 3333333 A B 1 2 X Mi x dx dx 0 25 0 25 G

Find the area of the region bounded by the graphs of the given equations y 4x y x x 0 x 2 Set up the integral s that will give the area of the region Select the correct choice below and fill in any answer box es to complete the choice OA OB S Dax dx O C fo dx dx

The figure below shows level curves for production f x y as a function of the quantities x and y of two raw materials utilized The cost of the materials is 15x 20y thousand dollars What is the maximum production possible with a budget of 300 thousand dollars How much of each raw material should be purchased to achieve this maximum 20 15 10 5 Y 2000 CT 5 10000 20000 10 15 20 25 Enter the answers to the nearest integer The maximum production possible is i of x and J dollars of y should be purchased

y 19 cos 4x 6 Amplitude Period Phase shift F C

The figure f x A d T TTTTTTTTTT

The graph of y f x solid and its tangent line at x 0 dashed is shown a second point on the tangent line is also marked Assume f x is continuous 10 9 8 7 6 5 Find f x lim x 0 x f x lim 204e 4 10 9 8 9 1 1 5 6 8 9 10

Let y 8 sin 2x 6 What is the amplitude What is the period What is the phase shift NOTE If needed you can enter 7 as pi in your answers I Cal

Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or or TU xxx X

Evaluate sin 9x lim 20 e 1 Question Help Video Written Example M

olve the problem Round your answer if appropriate 31 Water is being drained from a container which has the shape of an inverted right circular cone The container has a radius of 4 00 inches at the top and a height of 8 00 inches At the instant when the water in the container is 6 00 inches deep the surface level is falling at a rate of 0 9 in sec Find the rate at which water is being drained from the container A 42 4 in 3 s B 36 8 in 3s C 24 3 in 3 s D 25 4 in 3 s

Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or o or 818

Evaluate the limit using L Hopital s rule lim 3x e t

If csc 0 1 and 0 0 2 then evaluate the following 10 1 sec 0 2 sin 0 3 cos 0 4 tan 0 5 cot 0 JI CI

If tan 0 and sin 0 0 then find a sin 0 b cos 0 c sec 0 d csc 0 e cot 0 FI PI A A

Suppose the angle is in the first quadrant 0 0 2 and cos 0 a csc 0 b cot 0 help fractions help fractions Find exact values as fractions not decimal approximations for the following

Solve the problem 30 A wheel with radius 3 m rolls at 17 rad s How fast is a point on the rim of the wheel rising when the point is 7 3 radians above the horizontal and rising Round your answer to one decimal place A 12 8 m s D 25 5 m s B 102 0 m s C 51 0 m s 30

Evaluate the following Give your answer as a fraction NO DECIMAL numbers If sin 0 0 0 2 then cos 0 equals tan 0 equals sec 0 equals

Evaluate the following expressions Note The answer must be given as a fraction NO DECIMALS If the answer involves a square root it should be entered as sqrt For instance the square root of 2 should be entered as sqrt 2 If cos 2 7 and tan 0 0 then sin 0 tan 0 cot 0 sec 0 csc 0 9

Evaluate the following expressions sin T cos tan 2 cot 2 sec csc 9 4

dA Find the amount A in an account with continuously compounded interest after t years if dt A 4 8 326 49 The differential equation is of the form Round to three decimal places as neer dy dt dy dt k M y dy dt with k dy ky ky M y ky rA A 0 8 000 and

From April through December 2000 the stock price of a company had a roller coaster ride The table below indicates the price of the stock in dollars at the beginning of each month during that period Find the average rate of change in price per month between June and September Round to the nearest cent as needed Month April May June July August September October November December Price 116 107 88 100 95 112 93 84 65 OA 12 00 per month OB 8 00 per month OC 8 00 per month OD 12 00 per month

function given in the graph below and that f is a piecewise function whose parts are either portions of lines or portions of circles as pictured 6 5 4 3 A 6 A 1 A 4 A 6 6 Let A be the function defined by A z f t dt X b Compute the followings A 6 1 a What does the Second FTC tell us about the relationship between A and f Write an equation to describe the relationship A 0 X 6 5 X 3 2 1 2 3 5 X c Compute the followings 4 X a

If 0 7 then 4 sin 0 equals cos 0 equals tan 0 equals sec 0 equals

A company determines that its weekly online sales S t in hundreds of dollars t weeks after online sales began can be estimated by the equation below Find the average weekly sales for the first 5 weeks after online sales began S t 6et The average weekly sales amount is Round to the nearest cent as needed

Suppose the temperature in degrees Celsius over a 9 hour period is given by T t 1 7t 39 a Find the average temperature b Find the minimum temperature c Find the maximum temperature a The average temperature is degrees Type an integer or a decimal Round to one decimal place as needed

Which of these graphs is the graph of y x What is its domain Graph A Graph B Q O graph D 0 00 N graph C 4 3 2 1 0 1 2 3 4 graph A 00 00 A N Graph C Q N Graph D Ay