Differentiation Questions and Answers

Simplify the following expression sin x cos x sin x cos x sin x cos x sin x cos x Simplify your answer
Calculus
Differentiation
Simplify the following expression sin x cos x sin x cos x sin x cos x sin x cos x Simplify your answer
Simplify the given expression 3 COS NI X 3 cos 2x x 0
Calculus
Differentiation
Simplify the given expression 3 COS NI X 3 cos 2x x 0
Evaluate the integral 1 8x 3 dx 2610 2500 2572 2648
Calculus
Differentiation
Evaluate the integral 1 8x 3 dx 2610 2500 2572 2648
dA Given dt account after t years 0 02A and A 8000e0 02t
Calculus
Differentiation
dA Given dt account after t years 0 02A and A 8000e0 02t
Find the general or part dx 7x Whe dt O c 6
Calculus
Differentiation
Find the general or part dx 7x Whe dt O c 6
Evaluate using integration by parts x In x2 In 3x dx Ox In 3x x C Ox In 3x 2x4 C In 3x x C Ox In 3x x3 C HOTE
Calculus
Differentiation
Evaluate using integration by parts x In x2 In 3x dx Ox In 3x x C Ox In 3x 2x4 C In 3x x C Ox In 3x x3 C HOTE
Evaluate the definite integral to two decimal places 5 for e t dt 0 99 145 69 0 36 147 41
Calculus
Differentiation
Evaluate the definite integral to two decimal places 5 for e t dt 0 99 145 69 0 36 147 41
Find the intervals on which f x is inc f x x 27x 7
Calculus
Differentiation
Find the intervals on which f x is inc f x x 27x 7
The indefinite integral can be found in more tha integral Then find it without using substitution 9x8 x 8 dx
Calculus
Differentiation
The indefinite integral can be found in more tha integral Then find it without using substitution 9x8 x 8 dx
Find the indefinite integral and check the x x 3dx
Calculus
Differentiation
Find the indefinite integral and check the x x 3dx
Find the indefinite integral and check the result x 4 2x dx Determine an appropriate substitution to simpli 2 8
Calculus
Differentiation
Find the indefinite integral and check the result x 4 2x dx Determine an appropriate substitution to simpli 2 8
This graph shows a External tool lationship 5 4 3 2 1 y 5 4 3 2 1 2 31 4 5 etween x 1 2 y 3 4 5 Based on the graph when the value of v is 10 the value of x is
Calculus
Differentiation
This graph shows a External tool lationship 5 4 3 2 1 y 5 4 3 2 1 2 31 4 5 etween x 1 2 y 3 4 5 Based on the graph when the value of v is 10 the value of x is
Please show all your work NO WORK NO CREDIT Find the domain of y log 4 2x The domain is
Calculus
Differentiation
Please show all your work NO WORK NO CREDIT Find the domain of y log 4 2x The domain is
Previous Problem Problem List 1 point You are blowing air into a sp little Assume the radius of your ballo respectively Assume the thickness o r t inches A t square
Calculus
Differentiation
Previous Problem Problem List 1 point You are blowing air into a sp little Assume the radius of your ballo respectively Assume the thickness o r t inches A t square
1 point A stone dropped a How rapidly is the are The area is increasing at b How rapidly is the are
Calculus
Differentiation
1 point A stone dropped a How rapidly is the are The area is increasing at b How rapidly is the are
Consider the function f x 4x 7x 2 a Find the average rate of change of the function between a X b Find f x using the limit definition of the derivative
Calculus
Differentiation
Consider the function f x 4x 7x 2 a Find the average rate of change of the function between a X b Find f x using the limit definition of the derivative
Find f x the third derivative of f a 3 f x 5x 2x 5x 4x 7 Find the third derivative
Calculus
Differentiation
Find f x the third derivative of f a 3 f x 5x 2x 5x 4x 7 Find the third derivative
2 For the function f x x 36 find t x Then find f 0 and f 3 Find f x 36 36 Select the correct choice below and if necessary fill in the answer box to co A f 0 312 1 Simplify your answer Type an exact answer OB f 0 is undefined Select the correct choice below and if necessary fill in the answer box to co
Calculus
Differentiation
2 For the function f x x 36 find t x Then find f 0 and f 3 Find f x 36 36 Select the correct choice below and if necessary fill in the answer box to co A f 0 312 1 Simplify your answer Type an exact answer OB f 0 is undefined Select the correct choice below and if necessary fill in the answer box to co
For the function f x 2x 3x To find f x first find f x
Calculus
Differentiation
For the function f x 2x 3x To find f x first find f x
700 feet of fencing is available for a rectangular pasture alongside a river the river serving as one side of the rectangle so only three sides require fencing Find the dimensions yielding the greatest area Enter your answers as a comma separated list
Calculus
Differentiation
700 feet of fencing is available for a rectangular pasture alongside a river the river serving as one side of the rectangle so only three sides require fencing Find the dimensions yielding the greatest area Enter your answers as a comma separated list
5 Identify the value of c that satisfies the Mean Value 3 2 Theorem for h x 4x 8x 7x 2 on 2 5
Calculus
Differentiation
5 Identify the value of c that satisfies the Mean Value 3 2 Theorem for h x 4x 8x 7x 2 on 2 5
4 Determine all the values of c for the function 2 f x x 5x 7 on interval 1 3 which satisfies the Mean Value Theorem
Calculus
Differentiation
4 Determine all the values of c for the function 2 f x x 5x 7 on interval 1 3 which satisfies the Mean Value Theorem
Find the following derivatives Express your answer in terms of the independent variables 2x 2z 3y 2z X s 2t y 3st and z s 2t w and w where w aw ax Type an expression using x y and 7 as the variables
Calculus
Differentiation
Find the following derivatives Express your answer in terms of the independent variables 2x 2z 3y 2z X s 2t y 3st and z s 2t w and w where w aw ax Type an expression using x y and 7 as the variables
Find the following derivatives z and z where z xy xy x 2s t and y 25 1 dz Type an expression using x and y as the variables
Calculus
Differentiation
Find the following derivatives z and z where z xy xy x 2s t and y 25 1 dz Type an expression using x and y as the variables
4 points A6 Curve Sketching Draw the graph of x y 1 x without using a calculator Note all important features of the graph Domain intercepts local maxima and minima inflection points concavity and asymptotic behavior
Calculus
Differentiation
4 points A6 Curve Sketching Draw the graph of x y 1 x without using a calculator Note all important features of the graph Domain intercepts local maxima and minima inflection points concavity and asymptotic behavior
Let f x cos 5x 3 sin 6x 5 Then f x 5 sin 5x 3 sin 6x 5 6 cos 6x 5 cos 5x 3 x You do not need to simplify your answer Question Help Video Written Example
Calculus
Differentiation
Let f x cos 5x 3 sin 6x 5 Then f x 5 sin 5x 3 sin 6x 5 6 cos 6x 5 cos 5x 3 x You do not need to simplify your answer Question Help Video Written Example
45 A hawk flying at 15 m s at an altitude of 180 m acciden tally drops its prey The parabolic trajectory of the falling prey is described by the equation y 180 x 45 until it hits the ground where y is its height above the ground and x is the horizontal distance traveled in meters Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground Express your answer correct to the nearest tenth of a meter
Calculus
Differentiation
45 A hawk flying at 15 m s at an altitude of 180 m acciden tally drops its prey The parabolic trajectory of the falling prey is described by the equation y 180 x 45 until it hits the ground where y is its height above the ground and x is the horizontal distance traveled in meters Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground Express your answer correct to the nearest tenth of a meter
If f x 5 cos 2 ln x find f x Find f 5
Calculus
Differentiation
If f x 5 cos 2 ln x find f x Find f 5
Find the integral 0 1 9 7 1 x4 6x C w 3x8 7x 6 dx 01 1x 3x4 6x C 09x9 7x4 6x C 9x 1x4 6x C
Calculus
Differentiation
Find the integral 0 1 9 7 1 x4 6x C w 3x8 7x 6 dx 01 1x 3x4 6x C 09x9 7x4 6x C 9x 1x4 6x C
Find f x if f x O O 3 x Of x x 19 C 28x 5 32 3 3 7 28x 5 3 3 and f 1 4
Calculus
Differentiation
Find f x if f x O O 3 x Of x x 19 C 28x 5 32 3 3 7 28x 5 3 3 and f 1 4
Find the integral x8 416x7 dx O x8 4 7 c C 0 1 1 x 8 4 1 x 8 c C 56 x8 4 C O 3 16 18 4 C 56
Calculus
Differentiation
Find the integral x8 416x7 dx O x8 4 7 c C 0 1 1 x 8 4 1 x 8 c C 56 x8 4 C O 3 16 18 4 C 56
Find the integral 3x8 7x 7 dx 9x9x4 7x C 09x9 7x4 7x C Ox x 7x C
Calculus
Differentiation
Find the integral 3x8 7x 7 dx 9x9x4 7x C 09x9 7x4 7x C Ox x 7x C
K Summarize the pertinent information obtained by applying the gr Find the domain of f x Select the correct choice below and if n A The domain is all real x except x Type an integer or a decimal Use a comma to separate B The domain is all real x Find the x intercepts of f x Select the correct choice below and A The x intercept s is are at x 3
Calculus
Differentiation
K Summarize the pertinent information obtained by applying the gr Find the domain of f x Select the correct choice below and if n A The domain is all real x except x Type an integer or a decimal Use a comma to separate B The domain is all real x Find the x intercepts of f x Select the correct choice below and A The x intercept s is are at x 3
Find and list all the errors in the solution shown below For each error explain why it is not correct If there are no errors write there are no errors Type your answer in the space pre 1 1 Find d dr Solution te 1 1 1 1 te 1 1 te 1 te 1 1 e te 1 te 1 1 e te 1 te e te te fe te 2 126 12e Pe 1 te re c
Calculus
Differentiation
Find and list all the errors in the solution shown below For each error explain why it is not correct If there are no errors write there are no errors Type your answer in the space pre 1 1 Find d dr Solution te 1 1 1 1 te 1 1 te 1 te 1 1 e te 1 te 1 1 e te 1 te e te te fe te 2 126 12e Pe 1 te re c
In the following exercises find the average value of the function over the given rectangles 6 f x y sin 2x cos 3y R x 0 7 f x y x 2y R 0 1 0 1
Calculus
Differentiation
In the following exercises find the average value of the function over the given rectangles 6 f x y sin 2x cos 3y R x 0 7 f x y x 2y R 0 1 0 1
If we know that g 2 1 and g 2 5 evaluate the numerical value of h 2 where h x g x 1 3
Calculus
Differentiation
If we know that g 2 1 and g 2 5 evaluate the numerical value of h 2 where h x g x 1 3
Write the first four non zero terms of the Taylor series representation of 1 x 5 x 1 centered at 0
Calculus
Differentiation
Write the first four non zero terms of the Taylor series representation of 1 x 5 x 1 centered at 0
54 5 2 3 The function graphed above is decreasing on the interval X x 2 X The inflection point is at x 5 5 X
Calculus
Differentiation
54 5 2 3 The function graphed above is decreasing on the interval X x 2 X The inflection point is at x 5 5 X
Use sigma notation to write the Maclaurin series for the function COS TIX
Calculus
Differentiation
Use sigma notation to write the Maclaurin series for the function COS TIX
10 a b Find the Taylor polynomial P4 for f x In x at xo 1 1 x 1 x 1 x 1 x 1 1 1 x 1 x D x 1 x 1 c x 1 x 1 x 1 x 1 1 d x 1 x 1 x 1 x 1
Calculus
Differentiation
10 a b Find the Taylor polynomial P4 for f x In x at xo 1 1 x 1 x 1 x 1 x 1 1 1 x 1 x D x 1 x 1 c x 1 x 1 x 1 x 1 1 d x 1 x 1 x 1 x 1
estion 4 2 points For each of the following series select the best series to compare for using the limit comparison test 00 n 1 9n n 3n 2n 1 n 1 1 N 2 3 A 9n 3n n 713 2
Calculus
Differentiation
estion 4 2 points For each of the following series select the best series to compare for using the limit comparison test 00 n 1 9n n 3n 2n 1 n 1 1 N 2 3 A 9n 3n n 713 2
43 46 Expressions Involving Inverse Trigonometric Func tions Write the given expression as an algebraic expression in x 43 sin 2 tan x 44 tan 2 cos x
Calculus
Differentiation
43 46 Expressions Involving Inverse Trigonometric Func tions Write the given expression as an algebraic expression in x 43 sin 2 tan x 44 tan 2 cos x
11 16 Lowering Powers in a Trigonometric Expression Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine as in Example 4 11 sin x 12 cos x 4
Calculus
Differentiation
11 16 Lowering Powers in a Trigonometric Expression Use the formulas for lowering powers to rewrite the expression in terms of the first power of cosine as in Example 4 11 sin x 12 cos x 4
Let f be the function defined by f x for f x sin t t dt Find an expression
Calculus
Differentiation
Let f be the function defined by f x for f x sin t t dt Find an expression
Match functions a through d with their surfaces below a f x y cos xy 1 x y c h x y b g x y In x y 1 d p x y 1 x y a Determine the graph of f x y cos xy Choose the correct graph below O A OB O C
Calculus
Differentiation
Match functions a through d with their surfaces below a f x y cos xy 1 x y c h x y b g x y In x y 1 d p x y 1 x y a Determine the graph of f x y cos xy Choose the correct graph below O A OB O C
Write a polynomial f x that satisfies the given conditions Polynomial of lowest degree with zeros of 4 multiplicity 3 3 multiplicity 1 and with f 0 960
Calculus
Differentiation
Write a polynomial f x that satisfies the given conditions Polynomial of lowest degree with zeros of 4 multiplicity 3 3 multiplicity 1 and with f 0 960
For 5 8 refer to the parallelogram Write answers only using a b c d and their multiples 7 d c O C Od Ob O d a O b 18 C b d
Calculus
Differentiation
For 5 8 refer to the parallelogram Write answers only using a b c d and their multiples 7 d c O C Od Ob O d a O b 18 C b d
For 5 8 refer to the parallelogram below Write answers only using a b c d and their multipl 8 2c b O d No answer text provided a 18 10 b
Calculus
Differentiation
For 5 8 refer to the parallelogram below Write answers only using a b c d and their multipl 8 2c b O d No answer text provided a 18 10 b
Using ALL your knowledge of rational functions sketch a graph of the following functions Use min and max critical numbers and table 1 b f x x 2x x 2
Calculus
Differentiation
Using ALL your knowledge of rational functions sketch a graph of the following functions Use min and max critical numbers and table 1 b f x x 2x x 2
Without using a calculator find all the solutions of 1 3 where t T tan t
Calculus
Differentiation
Without using a calculator find all the solutions of 1 3 where t T tan t