Differentiation Questions and Answers

4 2 points Find the differential dy for the function y 36x

a Use differentiation to find a power series representation for f x f x f x 1 n 1 x 5 2 n 0 What is the radius of convergence R R 5 b Use part a to find a power series for 1 5 x n 0 f x n 2 1 5 x What is the radius of convergence R R 5 1 n 2 n 1 x 5 5 c Use part b to find a power series for x 5 x What is the radius of convergence R R 1 n 2 n 1 x 5 5

Use the given information to find the exact function value Given csc e 119 169 120 169 120 169 119 169 13 12 and cos 0 find cos 20

Use a sum to product formula to find the exact value 11x 12 sin 00 O 29T N S 511 11211 sin

Solve the equation over the interval 0 2TT sin x 3sin X 4 0 O O 2

Differentiate the following function y ex d y ex 0 dx

Differentiate the following function y e 6 d dx 4 leto

Find the derivative y In 7 6x y PERING DIRE

Find the derivative of the function 12 y x 2 ex

Calculate the work in joules required to pump all liquid out of a full tank Assume a 6 m b 12 m water exits through the spout c 3 m the density of liquid is 1000 kg m and g 9 8 m s Use scientific notation Give your answer to three significant figures

What is the average rate of change of f x from x 4 to x 2 Please write your answer as an i integer or simplified fraction f x 2x 9 Answer

Use the reference angle to find the exact value of the following expression Do not use a calculator cos 225 Select the correct choice below and fill in any answer boxes in your choice O A cos 225 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression The answer is undefined OB

In a right triangle if the length of the hypotenuse is 51 and the length of one of the other sides is 24 what is the length of the third side Simplify your answer

dy Use the Fundamental Theorem of Calculus to find dx dy da E 5 sin x sin cos x COS X where y

Find the general indefinite integral Use an upper case C for a any arbitrary constants 3 2 2 1 ds 3 n 1 an 3 C 112 Answers Attempt 2 of 2 Answer

Use part I of the Fundamental Theorem of Calculus to find the derivative of h x NOTE Enter a function as your answer Make sure that your syntax is correct i e remember to put all the necessary er 1 rsin z h x cos t t dt

dy Use the Fundamental Theorem of Calculus to find dx dy where y 1z cos z COS

steel a machine is used to cut the bars to specific lengths The machine has a dial that sets the length of the bars to be cut However the dial is currently out of alignment and the plant manager is collecting data to assess the situation The table shows 8 trials at different dial settings with the actual output length of the bars that were cut All measurements are in millimeters Use the data to construct a least squares regression line to predict output length from dial setting Dial Setting 75 77 79 80 81 82 83 85 Output Length 78 79 82 83 85 83 86 88

Find the average value of f x Average value 3 23 3x on the interval 1 2

Let F x 1 5 tan t dt Use the Fundamental Theorem of Calculus to find F x F x 9

A stone is launched vertically upward from a cliff 448 ft above the ground at a speed of 48 ft s Its height above the ground t seconds after the launch is given by s 16t2 48t 448 for 0 st 7 When does the stone reach its maximum height Find the derivative of s

the critical points of the following function X f x x 1 Select the correct choice below and if necessary fill in the answer box to complete your choi OA The critical point s occur s at x Use a comma to separate answers as needed OB There are no critical points

Find the critical points of the following function f x 5x 3x 4 What is the derivative of f x 5x 3x 4 f x

An equation of an ellipse is given a Identify the center of the ellipse c Determine the value of b e Identify the endpoints of the minor axis g Determine the length of the major axis 1 Graph the ellipse Express numbers in exact simplest form 4x 25y 100 Part 0 8 Part 1 of 8 The center of ellipse is 00 OC b Determine the value of a d Identify the vertices f Identify the foci h Determine the length of the minor axis

Question 12 2 points Which graph matches the equation y log x 2 1 2 N 3 2 1 31 2 11 2 2 3 4 5 6 7 8 2 3 4 5 6 7 8 C

Assuming x 0 how can the expression 3x 2 6x 0 5x 0 be simplified

The graph of the equation x y Dx Ey F 0 is a circle or degenerate circle Select one O True O False

e points A 2 4 6 B 0 6 2 and C 4 8 6 what is the distance from point A to the midpoint of the line segment E istance is d your answer to the nearest hundredth units

A chemistry student needs to measure the density of a metal nugget by performing the following calculation 34 47g 26 7mL 20 4mL What is the density of the metal nugget reported to proper significant figures 5 g mL 5 47 g mL 5 471 g mL 5 5 g mL

Given the following graph A 12 10 8 6 4 2 2 0 0 2 y 5 5x 11 y 2x 5 5 y 2x 11 y 2x 5 5 3 What is the value of the equation of the trendline

Solve 1 3 1 4 1 7 2 3 1 12 02 4

Given the function f x cos 5 compute the right endpoint Riemann sum using n 5 on the interval 0 2 help numbers R5 WENG

A chemistry student measures two volume amounts using two different instruments a buret and a graduated cylinder The two volumes are the following Buret 23 45 mL Graduated Cylinder 31 3 mL What is the total volume measured by the student rounded to proper significant figures 55 mL 54 750 mL 54 8 mL 54 75 mL

What is the answer for 1 3x103 m x 3 4x102 m reported to proper significant figures and unit O 4 4x105 m 4 42x105 m 4 42x10 m 4 4x10 m

A student need to solve for T in the following equation P V T1 P2V2 T2 What is the correct way of rearranging the equation above to solve for T OT1 P2V T2 P1V2 OT1 P V1 P V T2 T1 P V T2 P2V2 T P V T2 P1V1

A student need to convert 44 21in to cm knowing that 1in 2 54cm What is the measurement in centimeters 100 cm 112 3 cm 112 cm 112 2934 cm

16 The rectangles in the graph below illustrate a left endpoint Riemann sum for f x The value of this left endpoint Riemann sum is 4 on the in and this Riemann sum select an answer an overestimate of equal to an underestimate of there is ambiguity irea of the region enclosed by y f z the z axis and the vertical lines z 2 and z 6

Simplify the following unit m3 x s m x s Oms 1 Om s 2 Om5s 5 m s 2

Solve the following equation for x 4x 3 O O Ox 16 0 X 64 3 64 3 x 12 x 12

The graph of f is shown below Click on a graph to enlarge it Evaluate the following integrals by interpreting them in terms of areas 2 1 a da a b f x dx c f x dx dz 2 4

The average of an electrician s hourly wage and a plumber s hourly wage is 30 One day a contractor hires an electrician for 8hr of work and the plumber for 7hr of work and pays a total of 446 in wages Find the hourly wage for the electrician and for the plumber Part 1 of 2 The electrician makes hr Part 2 of 2 X

What type of triangle is ABC 4 1 2 4 B 0 6 3 C 2 4 1 O equilateral O isosceles O scalene O not enough information

The region between the graphs of y x and y 6x is rotated around the line 6 The volume of the resulting solid is 4

Evaluate the integral with the order reversed S SA Y 4 y2 dx dy 2 0 04 O 2 32 430 32 3

Evaluate SS 4x y2dA for R x y 10 x 3 0 y 1 R O 15 24 12 12

O O O O SS32x y dy 450 30 480 450

Evaluate 6x y x 2y dy Ox x 2 Ox x 1 2x x 1 Ox 2x 1

Use Lagrange multipliers to maximize f x y z 24x 12y 24z subject to x2 y2 z2 324 max f x y z f 12 6 12 648 max f x y z f 12 12 6 576 max f x y z f 12 12 12 720 max f x y z f 6 12 12 576

Find the local extrema for f x y x2 2xy 4y 6x 6y 8 f 5 2 13 is a minimum f 1 1 1 is a minimum f 5 2 55 is a maximum f 0 0 1 is a minimum

Find the local extrema for f x y x3 12x y Of 2 0 16 is a minimum f 0 0 0 is a minimum f 0 0 0 is a maximum f 0 2 4 is a maximum