Application of derivatives Questions and Answers

13 28 Simplifying Trigonometric Expressions Simplify th trigonometric expression sin x sec x tan x 13 14 COs x sec X cot x

Verify the identity cot t cos t cot t cos t cot t cos t sin t cos t cos t cos t 1 1

A particle is moving around the plane with velocity vector mathbf v t t sin t cos t 2 t 6 text for infty t 0 X the particle is located at 1 1 what is the position function of the particle b At what time s will the particle be located on the axis c In which general direction is the particle moving at t 0 left right and or down up d Find the equation of the line tangent to the particle s path at

Question 10 6 points It is allergy season When an average adult takes a allergy medication the serum level in the adult s b The amount of the drug in the bloodstream then d a Write an equation to model the decay of Zyrtec answer into the space below 2 points b Create a table or use your equation to show ho body 12 hours after taking a single dose Please ei get your answer in the space below or type your e

Power and quotient rules with Simplify 2x 6 2 4x 3 3 Write your answer using only positive expo

The daily production cost C for x units is modeled by the equation C 200 7x 0 345x 2 Explain how to find the domain and range of C

3 The image below shows the graph of a function f x Which is which

For each of the following situations compute the missing amount a Assets b Assets c Assets d Assets 54 400 Liabilities 85 500 Liabilities 52 000 Liabilities LA Liabilities Net worth Net worth Net worth Net worth 21 200 18 900 46 700 LA 16 000 S 54 800

Kara George received a 7 000 gift for graduation from her uncle If she deposits the entire amount in an account paying 5 percent what will be the value of this gift in 9 years Use Exhibit 1 A Round time value factor to 3 decimal places and final answer to nearest whole dollar Value of the gift in 9 years A

8 Use polar coordinates to evaluate the following integrals a b 5 25 y LV 0 25 y 11 A Y dA D x y x2 where y x y dxdy D is the region outside the circle of radius 1 centered at the origin and inside the circle of radius 1 centered at 0 1

A ball is thrown into the air and its position is given by h t 7 7t2 91t 20 where h is the height of the ball in meters t seconds after it has been thrown Find the maximum height reached by the ball and the time at which that happens 288 87 5 00 meters

Find the critical numbers of the function f x 6x5 15x 50x 4 and classify them using a graph x 11 X x is a Select an answer O is a Select an answer is a Select an answer

Suppose f x and f x are continuous everywhere and have the following values 0 10 20 10 8 10 X f x Based on this determine what you are willing to guarantee Between 0 and x 10 you guarantee Select an answer Between 10 and x 20 you guarantee Select an answer Between x 20 and x 30 you guarantee Select an answer Select an answer Between x 30 and x 40 you guarantee C C C 30 7 14 40 14

5 4 3 2 1 4 3 2 1 2 3 4 1 2 3 4 a The function graphed above is Increasing on the interval s ert Decreasing on the interval s

Consider the following f x x35x2 5 a Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero Select all that apply 2 1 1 0 0 1 1 2 4 5 b Adjust the table to approximate the zeros of the function Use the zero or root feature of the graphing utility to verify your

Mark the critical points on the following graph 5 4 3 36 27 18 2 1 18 27 36 Clear All Draw Dot 2 3 4 LLA 5

Given the function below f x 36x 9 Find the equation of the tangent line to the graph of the function at x 1 Answer in mx b form L x Use the tangent line to approximate f 1 1 L 1 1 Compute the actual value of f 1 1 What is the error between the function value and the linear approximation Answer as a positive value only error Approximate to at least 5 decimal places

The linear approximation at x 0 to sin 3x is A Bx where A is and where B is

b The future value of 900 saved each year for 10 years at 7 percent Round time value factor to 3 decimal places and final answer to 2 decimal places Future value 13 845 00 x

Use l near approximation i e the tangent line to approximate 49 3 as follows Let f x x Find the equation of the tangent line to f x at x 49 L x Using this we find our approximation for 49 3 is NOTE For this part give your answer to at least 9 significant figures or use an expression to give the exac

1 0 204 1 and find Use linear approximation i e the tangent line to approximate as follows Let f x the equation of the tangent line to f x at a nice point near 0 204 Then use this to approximate x 1 0 204

The line tangent to the graph of y at x 64 will have equation y This means Consequently

ST Ch 3 derivatives docx Open in Word ne the equation of the tangent line at x 8 1 form

Search TEST Ch 3 derivatives docx Open in Wor 1 donote the area length of a side

Consider the differential equation x y xy y 0 cos In x sin In x 0 Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval The functions satisfy the differential equation and are linearly independent since W cos In x sin In x Form the general solution y F 0 for 0 x

Verify that the given two parameter family of functions is the general solution of the nonhomogeneous differential equation on the indicated interval 2x y 5xy y x x y x x 1 2 2 1 x x 0 0 15 1 The inctions x 1 2 and x satisfy the differential equation and are linearly independent since W x 1 2 x set of solutions of the associated homogeneous equation and yp 0 for 0 x So the functions x 1 2 and x 1 form a fundam is a particular solution of the nonhomogeneous equation

Consider the differential equation y 2y 10y 0 e cos 3x e sin 3x Verify that the given functions form a fundamental set of solutions of the differential equation on the indicated interval The functions satisfy the differential equation and are linearly independent since W e cos 3x e sin 3x Form the general solution y 0 for x 0

For the quadratic function identify is none f x x 2 2 2

2319 N Cleveland Ave This historic rowhome is ideally located on one of the prettiest streets in Chicago s desirable East Lincoln Park neighborhood Nearby Clark Street is host to shops salons and spas cafes restaurants and bars The Big Apple grocer is just two blocks away and a Whole Foods Market is slated to open in early 2015 on nearby Fullerton Avenue Just three blocks east is Lincoln Park offering the Conservatory the Nature Museum the Zoo Diversey Harbor and the lakefronts North Avenue Beach and 18 mile trail 2319 N Clark is within the attendance areas of the highly rated Lincoln Elementary School and Lincoln Park High School a Construct an amortization table assuming a loan for 1 376 000 over 30 years at an annual interest rate of 3 85 2 points b What is the monthly payment c What is the total amount paid after 30 years d For comparison purposes look at a 15 year mortgage at 3 17 for 15 years Construct an amortization table assuming a loan for 1 376 000 over 15 years mortgage at an annual interest rate of 3 17 2 points e What is the monthly payment f What is the total amount paid at the end of your loan if you decide on the 15 year mortgage g Which loan is better 30 years at 3 85 or 15 years at 3 17 Explain

1 If f 2 2 and f 2 7 Let f a be the inverse function of f x f 2 Write the equation of the tangent line to f x at x 2

olve the quadratic equation x 6x 72

f x x 5x 7 and f 3 49 Let g x be the inverse function of f x g 49 Write the equation of the tangent line to g x at x 45 Y

Question 8 142 If f x 8x ln 4x then f x f x x 5 x

Find the deriative y arcsin 5r dy dr

5 4 3 2 1 0 1 2 3 4 5 6 4 42 0 1 2 3 0 3 6 9

An eraser weighs 17 4 grams A box with 44 erasers weighs 0 769 kg What is the weight of the box alone Please express your answer in grams

A 50 cm long candle burns at the rate of 40 mm every 45 minutes How long will the candle be after it has burned for 3 hours Please express your answer in centimetres

The length of a city block is 500 metres How many city blocks are in 1 00 km

If 1 box of erasers weights 300 grams 14 boxes of erasers weighs kg

Asimtot tegak Fungsi y O 4 dan 1 2 dan 1 O 2 dan 2 O 1 dan 4 2 dan 1 x 3x 2 x 4

A nurse is asked to administer 126 millilitres of drug That is the same as litres

Your pencil is 370 mm in length It is cm long

If a pencil weighs 0 085 kilograms it weighs g

a Cos x b Sin x C cos sin x d cosecx P cosecx

2 Points DETAILS Find the absolute extrema

es jointly as x and z and inversely as the product of w and p where y 2 45 when x 2 z 15 w 5 and p 27

Use integration by parts to evaluate the integral

Use the graph to find the vertical horizontal or oblique asymptote if it exists If there is more than one asymptote separate them using a comma If an asymptote does not exist enter in DNE Vertical Asymptote x Horizontal Asymptote y Oblique Asymptote y

1 Suppose the graph of fi flou 3

7 Suppose the graph of f A y f x 7 2 shift 2 units to