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

Simplify the given expression 3 COS NI X 3 cos 2x x 0

Evaluate the integral 1 8x 3 dx 2610 2500 2572 2648

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Without using a calculator find all the solutions of 1 3 where t T tan t