Differentiation Questions and Answers

Find the derivative of the function y 5 8e4x y

Choose the graph of y log x Submit Question s 6 6 6 s K

1 Solve for x 1 Point sin x 1 27 x 2J O x x x 2 0 7 2 J O x 2 37 O x 7

Which of the choices below is an asymptote of the equation y 2 6 0 2 1 2 63 6

2 Small quantities of hydrogen can be prepared by the addition of hydrochloric acid to zinc A sample of 195 mL of hydrogen was collected over water at 25 C and 753 torr What mass of hydrogen was collected Pwater 24 torr at 25 C

Below is the graph of the derivative f x of a function defined on the interval 0 8 You can click on the graph to see a larger version in a separate window Refer to the graph to answer each of the following questions For parts A and B use interval notation to report your answer If needed you use U for the union symbol A For what values of x in 0 8 is f x increasing If the function is not increasing anywhere enter None Answer B For what values of 2 in 0 8 is f x concave down If the function is not concave down anywhere enter None Answer C Find all values of x in 0 8 is where f x has a local minimum and list them separated by commas in the box below If there are no local minima enter None Local Minima D Find all values of x in 0 8 is where f x has an inflection point and list them separated by commas in the box below If there are no inflection points enter None

Consider the function A Find the first derivative of f f x f x e 5 ez B Use interval notation to indicate where f x is increasing NOTE Use Inf for oo Inf for 00 and use U for the union symbol Increasing C List the coordinates of all local minima of f If there are no local maxima enter NONE values of local minima E Find the second derivative of f f x D List the x coordinates of all local maxima of f If there are no local maxima enter NONE values of local maxima

Consider the function f x 7 22 on the interval 2 6 Find the average rate of change of the function on this inter i e 6 f 2 6 2 By the Mean Value Theorem we know there exists a c in the open interval 2 6 such that f c is equal to this average ra of change For this problem there is only one c that works Find this value of c C

Find the indefinite integral using a table of integration formulas x 9dx x x 9 1n x x 9 c Ox x 9 91n x x 91 C Ox x 9 m x x 9b c Ox x 9 9 m x x 90 c

Consider the function f x 6x 1 0 x 2 This function has an absolute minimum value equal to which is attained at x and an absolute maximum value equal to which is attained at r 0

Find the x coordinate of the absolute minimum for the function f x 5x ln x 9x x 0

A Draw a 500 degree angle What is one positive angle that it is coterminal with this angle AS02 navn DA

The region in the first quadrant bounded by y 2x 2x y 4 and the y axis is rotate about the line z 1 The volume of the resulting solid is

ype answer rounded to 1 d p with one space between the number and the units For example 3 5 rpm 287 6 rpm Belp Lecture 84 Ex 84 5 13M What is the rotation rate in rpm of a 20 inch radius tire traveling at 100 ft per second Round to 1 d p

107 For h t 4e 0 3t cos 2t in Ex 87 1 what is the minimum value of t for which h t damp out to values less than or equal to 1 Select one 3 63 3 23 3 53 3 43

1282 Given that tan A B sin A B sin Acos B cos Asin B I cos A B cos Acos B sin Asin B by dividing every term by cosAcosB Select one tan A tan B 1 tan Atan B tan A tan B 1 tan Atan B tan A tan B 1 tan Atan B tan B tan A 1 tan Atan B derive an identity for tan A

99 Find f x if f x 4x sinx e 10 91 Select one O O O 60x cos2 9x4 ex cosx ex 20x4 cos 20x4 cosx te 1 X

57 Use Leibniz s notation to find Select one 9t xcosx 6sin2x cosx 9cos x Jain2naoan dy dx if y 3t and t sin

795 Find y if y e sin x Select one O O e cosx sinx In cos sinx e cos sinx ex cosx

66 Find g x if g x 96 Select one O O O 6x 13 x 1 13 x 1 6x 13 x 1 7 x 1 3x 10 X 1

10 Find the derivative of h x x sinx Inx 11 Select one 7x 7 7x 7 1 7x 7 1 7x 7 1 sinx cosx x 1 cosx X cosx x X

Lety In 1 cos x Then the value of 1 0 3 4 1 cos x 2 d y 2 dx e2 4 2 1 cos x equals 4 1 cos x

59 Find the symbolic form of the function expressed in the graph of f x Select one Of x x 1 2 O f x x 1 1 O f x x 1 2 f x x 3

595 Find the derivative of y e cosx Select one O O O O sinx ex cosx ex sinx ex cosx ex e cos sin

10g5 Decompose the ratio 85 Select one 21 12 2 2 2 2 1 2 2 2 7 2 7 20 2 x X 8 NIX 2 2 x 1 2 X 1 2 2 x 2 2 x 2 2 x 3x 4 4x x into a sum of partial fraction

Find f 2 for the piece wise function f x x 2 if x 1 2x 4 if x 1 f 2

Help Lecture 92 Lesson 92 and Ex 92 1a 692 Use definite integrals to find the exact area under the curve over the interval 1 f x x

296 Find 96 Select one O if y dx 2 3x lnx x Inx 2 3x lnx x Inx 2 4 3x lnx x 2 Inx 3x lnx x In x

7 Find the derivative of y In x sin x x 91 Select one 1 X O 1 X 1 X 8 COSX COSX 3x 3x x cosx 2x cosx 3x C

1574 Graph the hyperbola shown Calculate the eccentricity and find the equations of the asymptotes Select one O O eccentricity 29 asymptotes y 30 eccentricity 21 asymptotes y 1 c eccentricity 29 asymptotes y x eccentricity 31 asumptates 4 r y 2 95

Help Lecture 1475 Which of the following is the graph of x 3y 5x 4y 1 0 A Select one A B 0 1 D jek

characters Examples include 3 5 8 5 and 9 15 16 15 Hint Both x and y are fractions Help Lecture 83 Ex 83 1 1183 Use Cramer s Rule to solve the system of equations shown Write answer as an x y pair 3x 4y 2x 7y

Help Lecture 43 Ex 43 2 18 Using the figure shown find f g 2 10 5 10 8 6 g x f x 3

Find f 3 for the piece wise function f x x 2 if x 2 x 1 if x 2 f 3

18 Find all roots for g x 6x 13x 3x 2 Assume 1 root is a rational root which you can find using the rational roots theorem or your graphing calculator elect one x 2 1 1 2 23i 12 x 2 1 22 x 1 x 1 12 23i 12 23i 12 10i 12

Find f 2 for the piece wise function f x 2x 2 x 4 if x 0 if x 0 f 2 2

Identify the domain of the follov a log 6x 9 Domain b x ln 2x 3 Domain c f x log3 5x 3

Type answer as a whole number no decimals with one space between the number and the units For example 6 ft 18 ft Help Lecture 86 786 Animal Science As a way to gather speed and soar the albatross would rise and above the sea surface according to the periodic pattern h t 10 6 2 cost feet If t is in seconds find the albatross height after 6 seconds No GC

1850 If f x x 2 5 and g x f x 2 evaluate g x Ax 59 Select one O x Ax 5 O O x Ax O x Ax 5 x Ax 2

11 80 O Select one F F F F M TT Evaluate f x Arccscx when x 3 2 3 77 4 5T 4 Write answer

1641 Find all roots for f x 2x 3x 6x 4 Assume 1 root is a rational root which you car find using the rational roots theorem or a graphing calculator lect one D X 0 5 1 3i x 0 5 x 2 3i x 0 5 1 3i x 1 3i

Help Lecture 77 Ex 77 1 10 1 Find x Round to 1 d p 8 8 40 to 7

What are the dimensions of the rectangle with largest area that can be drawn inside a circle of radius 5 help numbers Width Height

Find the maximal area of a right triangle with hypotenuse of length 600 help numbers

KS Noureldin Aly Homew cgi x Isl exe 1o u lgNslkr7j

Use the fundamental identities and appropriate algebraic operations to simplify the following expression 3 tan x 3 tanx sec x 3 tan x 3 tanx sec x Type an integer or a simplifind fragtion X

Simplify the expression by using appropriate identities Do not use a calculator sin 73 cos 17 cos 73 sin 17 sin 73 cos 17 cos 73 sin 17

Write the logarithm as a sum or difference of logarithms Simplify each term as much as possible Assume that all variat numbers 1086 2160 3 b c b 5 1 0 ola 5

Simplify the expression to a numerical value 1 sin 0 1 sin 0 1 sin 0 1 sin 0 1 sin 0 1 sin 0 1 sin 0 1 sin 0 4 tan 0 2 4 tan 0

Verify the following identity COS T 2 Which of the following four statements establishes the identity OA cos 0 0 17 2 OB cos 0 OC cos 0 OD cos 0 2 sin 0 2 IN cos 0 cos sin 0 sin sin 0 2 2 sin 0 cos sin 0 cos cos 8 cos T 2 RIN 2 T 2 cos sin 2 cos 0 sin sin 8 sin RIN 2 T 2 sin 0 sin 0 sin 0