Differentiation Questions and Answers

Find the derivative of the function y 5 8e4x y
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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
Calculus
Differentiation
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