Application of derivatives Questions and Answers

Find the exact value of each of the remaining trigonometric functions of 0 2 6 sin given that cos 0 0 Select the correct choice below and if necessary fill in the answer box to complete your choice ACCESS OA cos 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice OA csc 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice OA sec 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice Find the exact value of each of the remaining trigonometric functions of 0 2 6 sin 0 given that cos 0 0 i wy OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice KIXE OA sec 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice OA tan 0 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression B The function is undefined Select the correct choice below and if necessary fill in the answer box to complete your choice OA cot 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The function is undefined

Tunction graphed to the right is of the form y a tan bx or y a cot bx for some a 0 b 0 etermine the equation of the function Half and quarter points are identified by dots an equation of the function shown is y Ay IN

Solve the equation Round to the nearest thousandth 3e5x 3 12 O A 0 323 OB 0 766 OC 0 877 OD 3 000

Use the Laws of Logarithms 2 In 2 4 In x In x to combine the expression In In x 5

Use the Laws of Logarithms to evaluate the expression log3 135 log3 45

2 5 Find a vector equation and parametric equations for the line 2 The line through the point 6 5 2 and parallel to the vector 1 3 3 3 The line through the point 2 2 4 3 5 and parallel to the vector 3i 2j k

Find the exact global maximum and minimum values of the function f x x for x 0 If there is no global minimum or maximum enter NA The global minimum is The global maximum is

Let A x f t dt where is the function given by the graph below 2 1 4 3 2 1 1 IN 3 A 4 2 A 7 Question Help Video Add Work 5 6 4

a Find the values of x for which f x has a local maximum Enter your answers in the increasing order x 11 x MI i eTextbook and Media b Find the value of x for which f x has a local minimum

How many inflection points are there There is are f x p inflection point s

Use derivatives to find the critical points and inflection points f x 5x 2 Inx Enter the exact answers in increasing order If there is only one critical point enter NA in the second area If there are no inflection points enter NA Critical points X X Inflection point

The figure below is the graph of a second derivative What are the x values that are inflection points of f L Enter your answers in increasing order X i f

Find the inflection points of f x x x 30x 2 Enter the exact answers in increasing order X

22 The monthly payments P dollars on a mortgage in which A dollars were borrowed at an annual interest rate of r percent for t years is given by P f A r t Which of the following is true of the the function f P monthly A It is a INCREASING function of A and a INCREASING function of t B It is a INCREASING function of A and a DECREASING function of r A amount C It is a DECE NG function of r and a DECREASING function of t D It is a INCREASING function of r and a INCREASING function of A r interect years

5 tan 0 csc 0 cot 0 cos 0 sin 0 1

What is the volume in liters of 3 4 moles methane gas CH4 at 10 C and 1 60 atm Express your answer using two significant figures VAEO L

9 Anita has a tiles bx tiles and c unit tiles to represent the quadratic equation y ax wants to rearrange the tiles into square diagrams a How many diagrams should she make b How many tiles will go to each diagram c How many of those a tiles are needed for the width How many are needed for the length d What is the length and width of each diagram e What is the x coordinate of the vertex of the quadratic bx c She

Find the most general antiderivative of the function Check your answer by differentiation Use C for the constant of the antiderivative f x x 3 5x 3 F x 4 Submit Answer X

Units completed and transferred out Less beginning WIP Units started and completed Answer b Beginning WIP Units started and completed Ending WIP Equivalent units of production Equivalent units of production FIFO Method Direct materials 380 000 76 000 304 000 Answer Req b Cost assignment FIFO Beginning work in process To complete beginning work in process Direct material Conversion Total cost to complete Total cost to complete beginning work in process Started Completed Direct material Answer Req a Cost per Equivalent units of production FIFO Method Cost incurred this period Total costs Equivalent units of production Cost per Equivalent units of production Conversion Total cost of started completed Completed Transferred out Ending work in process Units A 76 000 304 000 98 000 478 000 Percent added B Costs EUP 35 100 85 EUP Cost per EUP Direct materials EUP 26 600 49 400 2 18 EUP C A B EUP Cost per EUP 26 600 304 000 83 300 413 900 3 09 1 278 951 1 278 951 Costs 413 900 EUP 3 09 Total cost 82 194 107 692 Total cost 304 000 3 09 939 360 304 000 2 18 662 720 Cost per EUP Total cost Conversion Percent added D E E 65 4 100 30 35 3 38 Conversion 84 84 38 226 003 189 886 415 889 1 602 080 2 017 969

Evaluate the integral by interpreting it in terms of areas 6 1 1x1 x dx

A record club has found that the marginal profit P x in cents is given by P x 0 0007x 0 34x 48 9x for x 500 where x is the number of members currently enrolled in the club Approximate the total profit when 300 members are enrolled by computing the 6 P x Ax with Ax 50 i 1 sum The total profit when 300 members are enrolled is approximately Round to the nearest cent as needed Marginal profit in cents 30 000 24 000 P x 0 0007x 0 34x 48 9x 18 000 12 000 6 000 0 to 0 X II III IV V VI 100 200 340 400 500 Number of members

1 point Every year during home football games the Carroll College fans do push up contests to see how many they can do Suppose that a curious stats student in the stands kept track of the number of push ups completed for several students of both genders Males 22 18 31 22 26 27 31 12 27 18 Females 31 24 14 11 24 6 11 8 16 2 1 Consider the hypothesis that males in this contest can do more pushups than females Use an 0 01 significance level to test the claim a What test method should be used A Two Sample z test B Matched Pairs t test OC Two Sample t test b The test statistic is 11 7172 c Is there sufficient evidence to support the claim that males can do more pushups OA Yes OB No 2 Construct a 99 confidence interval for the mean of the differences between males and females F

5 48 and 5 49 Determine by direct integration the centroid of the area shown 5 50 Determine the centroid of the area shown in terms of a 5 51 Determine the centroid of the area shown when a 4 in 5 52 Determine the volume and the surface area of the solid obtained by rotat ing the area of Prob 5 1 about a the line x 240 mm b the y axis 5 53 Determine the volume and the surface area of the solid obtained by rotating the area of Prob 5 7 about a the x axis b the y axis y a Fig P5 50 and P5 51 X

For the following exercise use the figure below to find the desired quantities 25 24 B 13 Find sin 2a cos 2a tan 2a sin 23 cos 23 tan 26

the following exercises determine if the given identities are equivalent 1 cos 0 1 cos 0 cos 0 sin 0 sec 0 1

7tan x y 3 Find an equation of the tangent line to the curve at the point 6 points

8 If g 3 4 and g x x g x for all find 3

7 Find an equation of the line tangent to the graph of e x 1 at the point where x 0

Question 17 a Convert the equation f t 130 1 35 to the form f t aekt k Give values accurate to three decimal places Question Help Video Message instructor

Question 15 Solve the given equation for x 35x 2 40 x

Question 14 If e 17 then x

Question 11 Evaluate the following expressions Your answers must be exact and in simplest form a In e b eln2 C eln 3 d In 00 1 e4 Question Help Video 1 Video 2 Message instructor

Question 9 Find the logarithm log 10

Evaluate using your calculator giving at least 3 decimal places log 820 Question Help Vide

For questions 6 7 8 use I Question 6 C Iz 3i 3 Question 7 C z 3i 1 Question 8 C z3i 4 C C C W C C W z 2z 1 z z C C W dz

Part 3 of 3 3 points Skipped eBook Print References Required information 3 Assign costs to the department s output specifically to the units transferred out and to the units that remain in work in process at period end Note Round Cost per EUP to 2 decimal places Cost assignment FIFO Beginning work in process To complete beginning work in process Direct materials Conversion Started and completed Direct materials Conversion Completed and transferred out Ending work in process Direct materials Conversion Total costs accounted for EUP EUP EUP Cost per EUP Cost per EUP 0 00 Cost per EUP Total cost Total cost 0 00 0 00 Total cost 0 0 0

3 is the matrix of T V V with respect to a basis H and S is the change of basis matrix from a basis 9 to H Find the matrix A of T with respect to G 1 2 2 8 33 S 1 2 B 3 4 37 A

3 A particle is moving with the given data Find the position of the particle a t 3 cost 2 sint s 0 0 and v 0 4

Suppose we want to evaluate the definite integral 16 r 2502 4r2 dr using the substitution u Part 2 2502 47 Part 1 Re write the definite integral in terms of the variable u and remember to use the limits of integration for the function u f r Then input the antiderivative of the integrand and the limits of integration you found Note Type your answers above in such a way that the lower limit of integration is less than the upper limit of integration

Find the area enclosed by the given curves 10x 1 x2 26 Find the area of the region between the curve y A 10 e10 B In 10 and the interval 3 x 3 of the x axis C 10 In 10 D 0

Solve the multiple angle equation Enter your answers as a comma separated list Let n be any integer sec 4x 2 X

Verify the identity algebraically Use a graphing utility to check your result graphically 3 3 csc 0 3 cot 0 3 cos 0 sec 0

4 Find two positive integers such that the sum of the first number and four times the second number is 1000 and the product of the numbers is as large as possible

Perform the addition and use the fundamental identities to simplify cos x 1 sin x tan x

Use a graphing utility to complete the table and graph the functions in the same viewing window Use both the table and the graph as evidence that y Y2 Round your answers to four decim Y cos x sin x tan x y2 sec x x Y Y2 4 3 Verify the identity algebraically 4 8 Y cos x sin x tan x cos x cos x cos x 5 3 5 8 6 3 6 8 7 3

Factor the expression and use the fundamental identities to simplify Use a graphing utility to check your result graphically 2 sec x 2 sec x 2 sec x 2

Use the fundamental identities to simplify the expression Use the table feature of a graphing utility to check your result numerically 8 cot x cos x

etermine by direct integration the centroid of the area b X y a y kx a X

Consider the function f x 4 2 8 on the interval 2 7 A Find the average or mean slope of the function on this interval 4 7 4 2 Average Slope B By the Mean Value Theorem we know there exists at least one c in the open interval 2 7 such that f c is equal to this mean slope Find all values of that work and list them separated by commas in the box below List of values 9 2 14 2

4 24 81 12 30 20 10 too q 10 f x x3 x 6x 20 3 18 2 B 937 g x 6x 768 12 D 343 12