Functions Questions and Answers

2 Consider the function f x y y x 16 i Determine an equation for the tangent plane to the surface z f x y at input 3 2 ii Use part i to estimate the number 1 98 3 3 01 2 16 by hand For fun ask a machine what this number comes out to and compare to your estimate are you close

1 Find c 0 such that the area of the region enclosed by the parabolas y x c and y c x is 90

A factory selling cell phones has a marginal cost function C x 0 01x 3x 229 where represents the number of cell phones and a marginal revenue function given by R x 429 2x Find the area between the graphs of these curves and x 0 What does this area represent total profit for 200 cell phones sold total profit for more than 200 cell phones sold total revenue for 200 cell phones sold for 200 cell phones cold

Sketch the region enclosed by y 5x y 7x and x 1 Find the area of the e region

Exercise 5 13pt Find the maximal domain and all the asymptotes of the following function 2x 7 a f z 3 b f x 1612 9

Ed Sloan bought a new Explorer for 22 000 He put down 7 000 and paid 290 for 60 months The total finance charge to Ed is 15 000 17 400 2 400 4 200 None of these

A 7 000 4 120 day note dated March 20 is discounted on July 15 Assuming a 3 discount rate the bank discount is 1 74 1 77 7 11 17 68 None of these

A 25 000 15 80 day note dated November 5 is discounted at National Bank on January 5 The discount period is 80 days 19 days 61 days 91 days None of these

Solve for t K 5 3 3 t for t 0

Cooper Corporation must evaluate two capital expenditure proposals Cooper s hurdle rate is 10 Data for the proposals follow Required investment Annual after tax cash inflows After tax cash inflows at the end of years 3 6 9 and 12 Life of project Proposal X Proposal Y 120 000 120 000 24 000 72 000 12 years 12 years What is the cash payback period for Proposal X For Proposal Y Hint For Proposal Y in what year 3 6 9 or 12 will the full original investment be recovered Round Proposal X answer to one decimal place if applicable Proposal X 0 years Proposal Y

when x 0 Exercise 4 5pt Decide if the following function is continuous 2x 3x when x 0 a f x 0 when 0 3x when x 0 b f x 0 when r 0 2x when a 0

Sketch a rational function subject to the given conditions Horizontal asymptote y 1 Vertical asymptote x 2 y Intercept x Intercept 3 0 Part 0 3 Part 1 of 3 Sketch the horizontal asymptote y 1 and vertical asymptote x 2 X G

a Investigate the existence of equilibrium point s for the following nonlinear difference equation xn 1 rxn 1 xn and state the condition under which an equilibrium is stable if it exists b Consider the following nonlinear difference equation for population growth kxn b k 0 xn 1 b xn i ii iii Does the population reach a steady state If your answer in i is yes is the steady state stable Discuss when a conclusion from your investigation is biologically meaningless c Discuss the equilibrium and stability of the balls in the following diagram

is 0 07 The estimated standard error of the sampling distribution is 0 04 What is the 95 confidence interval Use the critical value z 1 96 5 point Part 2 5 points 10 points Round all calculations to two decimal places Put lower bound in the first box and upper bound in the second box Question 8 Type numbers in the boxes Quit Smoking Previous studies suggest that use of nicotine replacement therapies and antidepressants can help people stop smoking The New England Journal of Medicine 10 points published the results of a double blind placebo controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking The target for quitting smoking was the 8th day of the experiment In this experiment researchers randomly assigned smokers to treatments Of the 175 smokers taking a placebo 31 stopped smoking by the 8th day Of the 254 smokers taking only the antidepressant buproprion 79 stopped smoking by the 8th day Calculate the estimated standard error for the sampling distribution of differences in sample proportions The estimated standard error

he volume of the solid whose base is the region bounded by y x y 1 and the y axis and whose cross sections perpendicular to the y axis are equilateral es

Find the volume of the solid whose base is the region bounded by y x y 1 and the y axis and whose cross sections perpendicular to the z axis are semicircles Volume

Determine whether the sequence is divergent or convergent If it is convergent find the limit If not state your answer as divergent an n 3 n 1

1 Design a multiple recursive generator Z a1Z 1 a2Zi 2 a3Z 3 mod m with m 8 192 Do not use a a2 a3 1 State the parameters for your generator

Find the Expected Value from the table Outcome Value 400 800 Probability 417 317

Use what you have learned about the local and end behavior of polynomials to graph the function below 2x x 7 x 4 Drag the points to the z intercepts of the function Then use the sliders to select the appropriate behavior at each zero

Find the volume of the solid obtained by rotating the region bounded by about the y axis y 2 sin 6x2 y 0 0 x

Solve the logarithmic equation for x Enter your answers as a comma separated list Round your answer to four decimal places In x 1 In x 2 1 x

Solve the equation Enter your answers as a comma separated list Round your answers to four decimal places x25x 3xe5x5x 0 x

81 For the demand function q 2 4 find E p and determine if demand is elastic inelastic or neither at p 4 p E p

The doubling time for the amount of sick people infected by a virus is 27 days If we begin with 54 sick people calculate the value of b to complete the model below which gives the amount of the sick people in t days f t 54 b Enter your answer for b in the box below rounded to three decimals

Find the inverse of the matrix if possible If an answer does not exist enter DNE in any cell of the matrix 141 4 15

Gravel is being dumped from a conveyor belt at a rate of 15 ft3 min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal How fast is the height of the pile increasing when the pile is 13 ft high Round your answer to two decimal places x ft min

Graph the polar equation Create a chart of many ordered pairs in polar form and plot the points to show your work r 4sin20

W X Classify the angle above and calculate the supplement of the angle

2 I 12 5 Points DETAILS Graph the function not by plotting points but by starting from the graphs below 9 x 10x 1 2 10 5 y 3 y 2 2 2 2 WebAssign Plot State the domain and range Enter your answers using interval notation domain range State the asymptote 2 4

True or False A polynomial function with integer coefficients can have bot rational and irrational zeros True False

Find all rational zeros of the polynomial and then find the irrational zeros if any Whenever appropriate use the Rational Zeros Theorem the Upper and Lower Bounds Theorem Descartes Rule of Signs the Quadratic Formula or other factoring techniques Enter you answers as comma separated lists Enter all answers including repetitions If an answer does not exist enter DNE P x 2x 19x3 53x 38x 8 rational zeros x Irrational zeros x

A graph of a function f is given f 1 0 2 a Find the local minimum value of f and the value of x at which it occurs x y Find the local maximum values of f and the values of x at which they occur x y x y smaller x value larger x value b Find the intervals on which f is increasing Enter your answer using interval notation Find the intervals on which f is decreasing Enter your answer using interval notation

A retirement account is opened with an initial deposit of 9 500 and earns 8 16 interest compounded monthly What will the account be worth in 40 years Round your answer to the nearest cent

Find the x and y intercepts of the graph Do not graph the equation y x 25 x intercept smaller x value x y x intercept larger x value x y y intercept x y

Solve the inequality Enter your answer using interval notation X 1 X 11 0

Determine la integral f sec x tan x dx Determine la integral sec x dx

y 52 Given the following graph Evaluate f 1 Solve for f x 3 x

Find a Cartesian equation of the surface that is defined in spherical coordinates by the equation 1 p sincpcos 0 1 to conclude that 7 3 it is a sphere centered at x y z lof radius R

Al Miler the owner of Al s Garage estimates that he will need 29 000 for new equipment in 15 years Al decides that he will put aside the money now so that in 15 years the 29 000 will be available His bank offers him 10 interest compounded semiannually Al must invest today 6 710 60 6 942 60 6 701 60 125 335 10 None of these

Evaluate the integral Remember to use absolute values where ap 49 x4 dx X

Consider a triangle ABC like the one below Suppose that A 59 C 64 and c 19 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

4 2 X I 3T 10 101 10

Suppose that the functions and g are defined for all real numbers x as follows f x 4x 4 g x x 6 Write the expressions for f g x and g x and evaluate f g 2 S 8 x 1 8 x X 1 8 2

Compute the value of the discriminant and give the humb teal solutions of the quadratic 2 ocuation 7x 3x 3

Use L Hoppital s Rule possibly more than once to evaluate the following limit lim 5sin 3t In 3t t 0

2 I 2 2 1 C 3 Graph in interval 0 2 y sin x

What is the axis of symmetry for the quadratic function 2 1 x 2x 12x 1

Consider the curve given by the 2 2 2 2 equation x y 2x 2y x 2 22 Find the equation of the tangent lin at 0 1

Multiply 7 10 b 70 7 b 70