Mathematics Questions and Answers July 04, 2020

1 2 c If k x g x AM 2 1 2 9 x 5 2 sl a x 4 2 MIN find k 1 3 points 1 6 The functions f x and g x are differentiable for all values of x Selected values for Cry and g x and their derivatives are shown in the chart above a If s x f x g x find 2 1 point b If h x f x g x find 1 2 points 4 d If f x e f x find 1 Leave your answer in terms of e 2 points

A company s marginal cost function is MC x given below where x is the number o Find the total cost of the first hundred units 6e 0 022 MC x

Use a graph to solve the equation on the interval 2x 2r List the solutions in increasing order from left to right on the x axis csc x 2 3 3 x X X X smallest value largest value

Without a calculator match each function with its graph y log x e ba y e 97 5 4 y log a Note In order to get credit for this problem all answers must be correct y Click on graph to enlarge D X

Graph the inverse of the provided graph on the accompanying set of axes You must plot at least 5 points Click the graph to make a point Click it again to erase 10 9 8 7 6 5 4 3 2 y 10 1 9 8 7 6 5 4 3 2 1 1 2 3 5 8 10 1 2 3 4 5 6 7 8 9 10 X

15 22 Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum values of f Use the graphs and transformations of Sections 1 2 autoade 1 2 15 f x 3x 1 x 3

13 In year 2015 the population of a town was an annual 12000 and it was growing at rate of 3 2 Use this information for following Questions a write an exponential function of form pct town ab P Population of the and Number of years to b use your function from part a find algebraically the year the population reach 20000

3 6 A linear function contains the points 2 5 and 15 20 Does the point 43 53 also lie on the line Explain 2

T Find T N and x for the plane curve r t 7ti 7 In cos t j 2 T t cost i sint j Type exact answers using radicals as needed N t sin t i cost j Type exact answers using radicals as needed cos t k t 7 Type an exact answer using radicals as needed

Graph the following function by starting with the graph of y x and using transformations shifting compressing stretching and or reflection 52 f x 4x Lan the graphing tool to graph the function

Let h x f x g x If f x 2a 2x 3 and g x x 3x 4 what is h 1

What is the resulting integral if the substitution v is applied to da 2 edu 2fe du 2 d Suntstelle WRANGLg star PERICU

Consider a triangle ABC like the one below Suppose that B 58 C 67 and a 30 The figure is not drawn to scale Solve the triangle Round your answers to the nearest tenth If there is more than one solution use the button labeled or A 0 b 0 c 0 or O X No solution

Calculate the Fourier series of the function f t 2 tl 0 1 2 It otherwise

Calculate the Fourier series of the function 1 21tl, 1 ltl 2

A car rental agency rents 200 cars per day at a rate of 30 per day For each 1 increase in rate 5 fewer cars are rented At what rate should the cars be rented to produce the maximum income What is the maximum income The rental agency will earn a maximum income of when it charges per day

Differentiate Hint Use the Extended Power Rule g x In x 9 g x

Differentiate. (Hint. Use the Extended Power Rule.) g(x) ( In

Examples 1 Find the slope of the tangent to the ellipse x 4y 25 at the point 3 2 2 The equation 5x 6xy 5y 16 represents and ellipse dy dx a Find at 1 1 b Find two points on the ellipse at which the tangent is horizontal

Problem Design the optimal conical container having a cover which hold 0 2m of oil a Find the dimensions r and h of the can that will minimize the cost of the metal to manufacture the container Answers r 0 4070m Height 1 15266m Volume 0 1999m Total area 2 08m b Repeat but without a cover Answers r m h m c Using calculus verify if it is the same as

A GPCRs activate G proteins by reducing the strength of GDP binding allowing GDP to dissociate and GTP which is present in much higher concentrations to bind What would happen if the affinity of Ga for GDP were reduced but the affinity for GTP remained unaffected Explain your reasoning make sure to explain the effect on amount of pathway signaling

Determine if the series converges or diverges Give a reason for your answer 2n 3n 7 n 1 Select the correct choice below and if necessary fill in the answer box to complete your choice V The series converges because the limit found in the nth Term Test is OA Type an integer or a fraction The series diverges because the limit found in the nth Term

2 Refer to the function below to do the problems that follow Do not use a calculator That is for each problem be sure to show your work or justify your answer f x x 2x15 2x 3 a State the domain Use interval notation 4 points b Give the equation of each VERTICAL asymptote 4 points

Evaluate the integral by interpreting it in terms of areas In other words draw a picture of the region the integral represents and find the area using geometry S 3x 10 dx Question Help Video Message instructor

Next question 17 If f x t Get a similar question You can retry this to dt then f x 17 Hint Remember that f a t d 1 to to dt 17 Find the derivative of g a sin 1 dt g x sin x

Consider a generic quadratic function f x ax b c with characteristics described below Determine the domain and range of f The vertex of the graph of is 24 6 a 0 The domain of is The range of f is

Solve the inequality algebraically x 7 x 9 X 0 The solution is Simplify your answer Type your answer in interval notation Use integers or fractions for any numb expression

For the function F x oblique asymptotes Ho a graph the rational function using transformations b use the final graph to find the domain and range and c use the final grap x 4 b The domain of the given function is 4 U 4 00 Type your answer in interval notation Use integers or fractions for any numbers in the expression The range of the given

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

1 Find the Taylor Polynomials of orders 0 1 2 and 3 generated by fat a for f x 1 x 2 a 0

3 Find the inverse of y x 3 and state its domain and range

3. Find the inverse of y and state its domain and range.

304 EXEMPLAR PROBLEMS MATHEMATICS 39 C 41 B 45 1 43 C 46 n B 47 AB 48 9 1 2 1 2 49 0 1 2 3 4 5 6 8 50 6 1 5 9 10 ii 1 2 3 5 6 7 9 10 31 AUB 53 True 57 True 38 C 42 B 2 3 2 3 EXERCISE 1 1 1 1 3 2 1 2 3 3 1 3 3 1 1 1 2 1 3 3 1 3 2 3 3 52 1 b ii c ii a iv f v d vi e 55 False 54 False 56 True 58 False 1 1 1 3 3 1 3 3 iv 1 1 1 2 1 3 2 1 2 2 2 3 3 1 i

Given p 6 2 and 6 10 5 find p b 7 6

Given 6,2 and g 10, 5 , find F i).

A stone is dropped into a lake creating a circular ripple that travels outward at a speed of 40 cm s a Express the radius r of this circle as a function of the time t in seconds r t b If A is the area of this circle as a function of the radius find A o r Aor t Interpret the answer found in part b O This formula gives the radius of the rippled area

Given functions f and g find f g f x 6x 2 g x 9x 7 OA 3x 5 OB 15x 9 OC 3x 9 OD 3x 5

Integrate the given function 5 5 1 X 18x 9x dx 1 x 18x 9x Tung an integer or a decimal Round to the nearest thousandth as nee dx

4 0 67 1 Points Find the point of inflection of the graph of the function If an answer does not exist enter DNE f x x x 3 2 2 x y DETAILS concave downward X DNE Need Help Read It Describe the concavity Enter your answers using interval notation concave upward 3 0 PREVIOUS ANSWERS LARCALC11 3 4 023

Discuss the validity of the following stat x 1 n 1 If n is an integer then is an antid Choose the correct answer below O A This is a true statement for all p OB This is a true statement for all n

2 Given f x x 12 and g x x 3 5 points svin sit worb A Find fog 5 points Smotenont Find gof 5 points

O Points 0 of 1 se limit methods to determine which of the two given functions grows faster or state that they have comparable growth rates 27 In x Inx Set up the functions as an expression of a limit to determine which grows faster lim X10 W

4 of 10 4 5 points Starting from a stop a mouse runs to the right first then comes to a stop for a few seconds and then runs to the left Consider the graphs below Graph A Graph C Graph B a 2 points Which of the above graphs could describe the position of the mouse as a function of time b 2 points Which of the above graphs could describe the

1 point Consider the solid that lies above the square in the xy plane R 0 2 x 0 2 and below the elliptic paraboloid z 49 x 3y Using iterated integrals compute the exact value of the volume

A tank contains 70 kg of salt and 2000 L of water Pure water enters a tank at the rate 12 L min The solution is mixed and drains from the tank at the rate 6 L min a What is the amount of salt in the tank initially kg amount b Find the amount of salt in the tank after 2 5 hours kg amount c Find the concentration of salt in the solution in the tank

3 Integrate G x y z x over the parabolic cylinder y x 0 x 2 Write the integral G x y z do as a double integral S SS G x y z do SSO dx dz S 0 z 1

3 Find an equation of the tangent line to the curve In a at the point 1 0

3. Find an equation of the tangent line to the curve at the point (1 ,0).

Graph the particular solution to Choose the correct graph OA y X dy x 2 that goes through 0 1 dx OB ST y OC y AT X

The parametric equations and parameter intervals for the motion of a particle in the xy plane are given below Identify the particle s path by finding a Cartesian equation for it Graph the Cartesian equation Indicate the portion of the graph traced by the particle and the direction of motion x cos 2t y sin 2t 0stst The Cartesian equation for the

find the given indefinite intergal state whether inte by Substitution or integrat integration by parts was used Please tell me if this parts or substitution dx use integration by L xex dx dx

he local and absolute extreme values of f r s c d P q a b Q Give the local extreme values of f Choose correct answer below OA There is no local extrema O B Local minima are q and s local max are b and d O C Local minima are b and d local maxima are q and s Give the absolute extreme values of f Choos correct answer below OA Absolute minimum is q OB

The costs of a company are represented by the function C x 0 22x 1 750 Its revenues are represented by function R x 4 1x Find the function that represents the company s profits Provide your answer below

The gross domestic product G of Switzerland was 685 4 billion dollars in 2013 Give a formula for G in billions of dollars t years after 2013 if G increases by a 4 per year G t b 6 billion dollars per year G t

Use the properties of logarithms to expand the expression as a sum difference and or constant multiple of logarithms Assume all variables are positive

Find and simplify the difference quotient f x 7 OA 1 OB 0 O C 1 OD 7 h f x h f x h 11 h 0 for the given function

Graph the function f x 5 sin x O GL y 41 O 41 2

Glaph the function. tix) vs sin(s)

at d its to point pposite A B the other side of the lake in the shortest possible time see the figure She can walk at the rate of 4 mi h and row a boat at 2 mi h For what value of the angle shown in the figure will she minimize her travel time G 11 A 0 2 B 2 C

Let f x x 2 and g x x 3 fog x I gof x help formulas help formulas

Let N,G F 2 and g() u (go help (formulas) help (formulas)

Current Attempt in Progress An oil company discovered an oil reserve of 400 million barrels The company plans that q t the rate of extraction of oil in millions of barrels per year at time t will be How long does it take to exhaust the entire reserve Round your answer to one decimal place t i q t a bt years a 40 b 0 5

A stone is thrown straight up from the edge of a roof 975 feet above the ground at a speed of feet per second A Remembering that the acceleration due to gravity is 32 feet per second squared how high is the stone 3 seconds later B At what time does the stone hit the ground C What is the velocity of the stone when it hits the ground

Use geometric formulas to find the unsigned area between the graph of y f x and the x axis over the indicated interval f x x 10 2 11 The area between f x and the x axis is

The concentration of a solution is defined as the amount of a substance divided by the volume of the solution Suppose a vat contains 18 kg of salt and 50 liters of water At t 0 water is added at a rate of 25 liters minute while salt is added at a rate of 9 kg minute A function giving the concentration after t minutes will be C t kg liter express

Use a linear approximation or differentials to estimate the given number Round your answer to two decimal places 32 05 4 5 Enter an integer or decimal number more Question Help Marcago in

A hoist mechanism raises a crate with an acceleration in m s a 1 0 25t where t is the time in seconds Find the displacement of the crate as function of time if v 0 m s and s 3 m for t 0 s The displacement of the crate is given by s Type an expression using t as the variable

Find the length of the major axis of Earth s orbit using Kepler s third law and the fact that Earth s orbital period is 365 256 days Use G 6 6726 10 Nm kg M 1 99 x 1030 kg and 3 14 Recall that 1 N 1 kg m s 11 The length of the major axis of Earth s orbit is km Do not round until the final answer Then round to the nearest thousand as needed

The graph of a polynomial function is given P x 12x 3x 1 6 4 y intercept x y y x y 6 4 2 2 4 6 2 4 a From the graph find the x and y intercepts If an answer does not exist enter DNE x intercepts x y smaller x value 6 X larger x value b Find the coordinates of all local extrema If an answer does not exist enter DNE

t Suppose that the annual sales S in dollars of a company may be approximated empirically by the formula S 30 000 e logarithmic derivative to determine the percentage rate of growth of sales at t 16 The percentage rate of growth is Round to one decimal place as needed C where t is the number of years beyond some fixed reference date Use a

Find the inflection point for the function shown below If there are more than one be sure to spearate them by using a comma If there is not an inflection point record DNE in the answer box If necessary round all numbers to two decimal places f x 2x 18x 96x 3

Find the area of the region that lies inside r 1 cos 0 and outside r 2 cos E

Find the area Of the region that lies inside r I coso and outside T 2 cost

Use any method to evaluate the integral x dx 3 x dx 3 2 2 x 49 X 49

Use any method to evaluate the integral. x dx X 49 x dx

Verify the identity csc x sec x cos x cot x tan x cos x sin x

oel the denuty. csc) v cot(x) tan(x) COS(X) Sln(x)

Find two numbers A and B with AB whose difference is 44 and whose product is minimizec A B

Find two numbers A and B (with A B) whose difference is 44 and whose product is minimize(

Find the amplitude and period of the function y 4 sin x amplitude period Sketch the graph of the function y 12 9 6 3 10 5 AAMA son 12 9 6 3 6x 9 12 3 5 10 10 y 10 9 12x 5 AA 12 97 6x 3x 3x 9x 12 157 10 x 10 12 9 6 3x y 10 5 10 3A 9x

Exercice III 10 Points Find the Fourier series of the function if 0 x if x T f x X

1 If x 0 and y 0 then 2x y al X

1. If O and y 0, then

20 w 2 w ce 22 g t t t 11 3

20. w 32(w Cue) 22.

Estimate the price of one barrel of crude oil on January 25 2016 and the rate at which the price was rising on that day Your answer for the rate should be in dollars per day The price of one barrel of crude oil on January 25 2016 was about Type an integer or a decimal rounded to two decimal places as needed Barrel Price of Crude Oil 30 29 28 27 26

Simplify the trigonometric expression sec x 1 sec x 84 222

Simplify the trigonometnc expression. sec2(x) 1 see (x) 84.222

the f x by dragging the blue points to the locations on the x axis that correspond to the zeros of the function Use the red point as a slider to select the number of zeros that your graph will show You may click on a point to verify its coordinates Provide your answer below 10 5 200 100 0 100 f x 2 x 5 x 1 x 8 10

K For f x a fog 6 X 5 5 and g x find the following composite functions and state the domain c x b gof c fof d gog a fog x 6x 5 1 x Simplify your answer Use integers or fractions for any numbers in the expression The domain of fog is 0 U 0 1 U 1 00 Type your answer in interval notation Use integers or fractions for any numbers in the exp your

Question A Use implicit differentiation to find the equation of the tangent line to the function defined implicitly by the equation below at the point 1 1 3x 4x 10 2y y Give your answer in the form y mx b

sin x Recall that tan x cos x Using integration by substitution to derive the derivative of tan x Edit

Write an expression for the apparent nth term an of the sequence Assume that n begins with 1 1 6 11 16 21 an

Find the area of the region under the graph of y and above the interval 1 3 223 320 81

A study examined brain size measured as pixels counted in a digitized magnetic resonance image MRI of a cross section of the brain and IQ 4 Performance scales of the Weschler IQ test for college students The scatterplot to the right shows the Performance IQ scores vs the brain size Describe the association between brain size and IQ as seen in the

Determine whether f x 4x 16x 4 has a minimum or maximum value and find the value of the minimum or maximum Also find the axis of symmetry The y value of the is The axis of symmetry for f x is given by help numbers help numbers

Determine if the geometric series converges or diverges If a series converges find its sum O A 9 Select the correct choice below and fill in any answer boxes in your choice 9 3 0 9 Simplify your answer OB The series diverges 5

0 10 For which values in the domain is this graph decreasing Give your answer in interval notation Assume the graph extends to infinity in both directions Try again 1 00 Edit my response

5 a Find the indefinite integral of each of the following i f 3 2x 3 dx

5. (a) Find the indefinite integral of each of the following. (i) J 3(2x 3)3dx

Solve the system of equations. You may use any method of your choice, but your method must be algebraic (not graphical). If the system is inconsistent, state there are no solutions. If the system is dependent, express the solution set by naming one coordinate as a and expressing all other coordinates in terms of a.2(x + 2z) = 2-y5z + 2 = y-x2x +

6 Apply the Intermediate Value Theorem to determine on which of these intervals the graph of f x 2x 7x 1 must intersect the line y 4 A 8 6 B 4 1 C 0 2 D 6 9 E Can t guarantee that it will intersect

Use the graph below to state a the domain b range c where it is increasing d and decreasing using interval notation e x intercepts f local max g and mins Estimate values that are not clearly marked f x 5 3 2 1 5 4 3 2 1 0 1 2 3 4 12 B 45

Biologists have observed that the chirping rate of crickets of a certain species is related to temperature and the relationship appears to be very nearly linear A cricket produces 120 chirps per minute at 70 F an 168 chirps per minute at 80 F a Find the linear equation that relates the temperature t and the number of chirps per minute n b If the

Question 3 b What is the y intercept The graph of f x 4 is reflected about the y axis and shifted upward 4 units a What is the equation of the new function g x g x c What is the domain d What is the range Question Help VIDEO Post to forum

Score 2 9 279 answered Question 8 f 5 Suppose that 4 f x 5 for all values of x What are the minimum and maximum possible values of 5 f 3 0 1 pt 6 f 3

Problem 1 Let f x 4x 2 and g x x 2 a Find the solutions to the equation f x 3 b Find the domains of f and g Argue why they are or are not injecti c Write fog d Find the inverse of f x e Calculate the first and second derivative of f x

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

c 5 pts Find the equation for the tangent line to f x at the point 1 3 x 2 obr tangent V

IF F x x 1 ar x 3 4x then

6 Suppose the monthly revenue in thousands of dollars for the sale of xhundred units of an electronic item is given by the function R x 40x e 0 4x 30 Determine the number of units to produce in order to maximize revenue

An employee s monthly productivity M in number of units produced is found to be a function of the number t of years of service For a certain product a productivity function is shown below Find the maximum productivity and the year in which it is achieved M t 3t 144t 140 0 t 40 The maximum productivity is achieved in year The maximum productivity

Find the volume of the solid bounded below by the circular cone z 1 y and above by the sphere x y 2 2 25z

Use the properties of inverse functions to find the exact value of the expression if possible Enter your answer in radians If an answer is undefined enter UNDEFINED COS

dr Let A be the area of a circle with radius r If dt dA dt 2 find when r 2