# Calculus Questions

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Calculus

Differentiation6 Use Logarithmic Differentiation to differentiate to find dy dx given 3 x x 1 x 2 x 1 2x 3 y

Calculus

DifferentiationLet f v v 5v Determine the critical values of f If multiple such values exist enter the solutions using a comma separated list Ov No critical values exist Submit Question

Calculus

Indefinite IntegrationGraph t rabola y x 6x 4 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a funct button 12 10 By 12 X D 5

Calculus

Definite IntegralsHow large should be to guarantee that the Trapezoidal Rule approximation to 1x 1 dr is 2 22 122 accurate to within 0 0001 n How large should n be to guarantee that the Simpsons Rule approximation to 2 27 127 17 1 dr is accurate to within 0 0001 n Hint Remember your answers should be whole numbers and Simpson s Rule requires even values for n Question Help Video 1 D Video 2 Message instructor

Calculus

Application of derivatives3 In estimating 1 error involved in the approximation using the Error Bound formulas cos 4x dx using Trapezoidal and Simpson s rule with n 8 we can estimate the For Trapezoidal rule the error will be less than For Simpson s rule the error will be less than Give your answers accurate to at least 2 decimal places Question Help Video 1 Video 2 Message instructor Calculator

Calculus

Definite IntegralsUse Simpson s Rule and all the data in the following table to estimate the value of the integral 1 10 F yda on 10 6 1 N N 4 Pa 0

Calculus

Definite IntegralsUse Simpson s rule with n 6 to approximate cos z dz Keen at least 2 decimal places accuracy in your final answer

Calculus

Definite IntegralsThe following table shows the rate of water flow in L min through a dam t min 1 6 V t L min 6 1 5 1 16 21 26 31 15 liters 69 5 Approximate the total volume of water that passed through the dam from t 1 tot 31 using Simpson s rule with n2 6

Calculus

Definite IntegralsA region bounded by f y y 4 y 1 and x 1 is shown below Find the volume of the solid formed by revolving the region about the y axis 3 2 1 5432 234 2 3 88 T 3 20n O 18n O 20 3 ob wit Nw T

Calculus

Limits & ContinuityWhat is f x given the integral function f x cos u du f x sin x o f x cos x sin x O o f x cos x o f x cos x O 34 35 36 37 38

Calculus

Vector CalculusConsider the function y 4 sin 2x 7 Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period T c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of 5 0 d The point 0 0 transformed into e The point 5 transformed into 0 0 f Graph the function 57 8 122 32 8 Clear All Draw ww X 4 2 3 4 54 T 2 A 718 T14 31 8 2 57 8 3TV

Calculus

Definite IntegralsWhich integral would represent the area shown The function is f x x 5 3 2 0 0 5 1 1 5 2 2 5 Created with a trial version of Advan O 2 24 x 5 dx 5 x dx 5 x 5 dx o f 5 x 5 dx O

Calculus

Definite IntegralsWhat is the Riemann sum that represents the illustration shown The function is f x x 5 o xi i 1 O O O xi Axi i 1 3 xi i 1 xi Axi i 1

Calculus

Application of derivativespoints possible graded For the given function f evaluate f 3 f 2 f 1 and f 0 f 3 2 f 1 f 0 f x x 4 2x 3 if x 2 if x 2

Calculus

Indefinite IntegrationWhich function matches the indefinite integral dx o F x 12 1 2x O F x C 4x F x C o F x 1 C

Calculus

Differential equationsFor the given function f evaluate f 1 f 0 f 3 and f 7 f x f 1 f 0 f 3 7 2x 3 if 2x 6 if x 0 x 0

Calculus

Indefinite IntegrationRewrite F x as F u using a substitution of variables F x f 6x 5 4 3x 5x dx o F u f4 du o F u f 4 du o F u f 42u du F u f 4 dx

Calculus

Indefinite IntegrationWhich of the following statements match the indefinite integral e dx of e dx C In x of et dx et C of e dx et of e dx e C T 2 3 LG 5 co 6

Calculus

Indefinite IntegrationConsider the function y 4 sin 2x x Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period T c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of d The point 0 0 transformed into e The point 1 transformed into f Graph the function 57 8 2 37 8 7 4 7 8 P 2 10 S 704 3 8 22 S 8 3x T

Calculus

Definite IntegralsWhat formula would be used to calculate the left rectangle approximation of 2x 2 dx using five subintervals O L5 0 4 2 0 2 2 2 0 6 2 2 1 0 2 2 1 4 2 2 1 8 2 O L5 0 4 2 0 0 2 2 0 4 2 2 0 8 2 2 1 2 2 2 1 6 2 O L5 0 4 2 0 4 2 2 0 8 2 2 1 2 2 2 1 6 2 2 2 0 2 O L5 0 2 2 0 2 2 2 0 6 2 2 1 0 2 2 1 4 2 2 1 8 2 A 20 21 22 23 24 25 26 27 28 29

Calculus

Definite IntegralsFind the area of the region bounded to the right by X y 4 and to the left by x y 2 R2 0 O 4 5 04 2 4 6 8 O 3 75 O 8 3 61 62 63 GA GE 66 67

Calculus

Limits & ContinuityWhat is the smallest angle of this triangle 12 23 34 Round to the nearest hundredth Ente

Calculus

Vector CalculusOSCAGC03s02q512P What is the domain of the function O 0 11 O 0 2 O 1 1 00 0 0 7 O f x 3 7 2x

Calculus

Indefinite IntegrationFor the slope field shown which could be a family of anti derivatives 3 2 111 O y x C O y x C o y x C oy e C

Calculus

Limits & ContinuityCalculate the exact value of sin 67 using the half angle formula Rationalize the denominator if necessary sin 67 5 Enter or Ent

Calculus

Limits & ContinuityGiven the angle 315 a Convert it as radian b Find its coterminal angles in degrees within 720 360 degrees and degrees Enter positive value first and Negative second c Draw the angle below Click the center of the circle then click the correct dot on the circumference 14 14 12 a 0 0 8 06 04 0 2 08 06 04 02 0 2 0 4 0 6 0 8 to 12 0 2 0 4 0 6 0 8 Q 12 14 24

Calculus

Differentiationthe following is the graph of f x the function f x has a local A 2 and 1 3 1 and 1 Q0 and 1 Dj 2 only E 1 only hj

Calculus

Definite IntegralsA region bounded by f y 2y 2 y 0 y 3 and x 1 is shown below Find the volume of the solid formed by revolving the region about the y axis 10 4234 2 3 4 5 6 7 8 9 O 36 O 63 O 242 T O 817

Calculus

Indefinite IntegrationAn object is moving along a horizontal path shown in the graph 5 3 2 2 3 4 5 114 AD What is the displacement of the object for the time interval 2 5 O Displacement is 5 O Displacement is 5 O Displacement cannot be determined from the information given O Displacement is 9

Calculus

Definite IntegralsRewrite the integral using substitution x cos x dx 25 5 cosu du O O O 25 5 cosu du 125 cosu du 125 cos u du 30 31 32 33 34 35

Calculus

DifferentiationWhich of the following graphs is the slope field for Plea 111 2111 2 3 4 5 dx cos x O O 11 1 A 543 11 MAX 2 3 4 5 24 04 1 123

Calculus

Application of derivativesFind the formula for the total distance traveled by an object with a velocity v t 21 8 on the interval 0 5 21 8 dt 21 8 dt 0 21 8 dt 2 21 8 dt O 0 21 8 dt 21 8 dt 21 8 dt 21 8 dt 55 56 57 58 59 60 61 62 63 6

Calculus

Limits & ContinuityFind the displacement of an object on the interval 2 t 5 if its velocity is shown O 8 5 O 10 O 10 5 O 14 5 KO in an

Calculus

Definite IntegralsAn object moves along a path with a velocity v t 1 t and the initial position of the object is x 0 2 What is the equation for the position of the object when the acceleration is zero 0 2 u u du 0 2 u du 0 2 u u du lo u u du 48 49 50 51 52 53 54 55 56

Calculus

Vector CalculusWhat is the sub reference function f x for the function f x 5 x 3 2 4 the function that handles the non rigid transformation of the parabola first O f x 5x 0 x x O f x 5 x 3 O f x x 3

Calculus

Indefinite IntegrationConsider the function y 4 sin 2x Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of T 2 d The point 0 0 transformed into 0 0 e The point f Graph the function 57 8 transformed into 37 8 N 7U4 7 8 718 74 1 2 X Clear All Braw 0 04 X 3782 57 8 37

Calculus

Definite IntegralsRewrite the integral using substitution O O O u du 68 10 1308 u du 68 u 0 du 64 u du 3 10 x x 4 0 dx 29 30 31 32 33 34

Calculus

Application of derivativesFind the area of this triangle 155 260 175 Round to the nearest whole number

Calculus

Application of derivatives0 A survey found that women s heights are normally distributed with mean 63 6 in and standard deviation 2 2 in A branch of the military requires women s heights to be between 58 in and 80 in a Find the percentage of women meeting the height requirement Are many women being denied the opportunity to join this branch of the military because they are too short or too tall b If this branch of the military changes the height requirements so that all women are eligible except the shortest 1 and the tallest 2 what are the new height requirements Click to view page 1 of the table Click to view page 2 of the table a The percentage of women who meet the height requirement is 99 46 Round to two decimal places as needed Are many women being denied the opportunity to join this branch of the military because they are too short or too tall OA Yes because a large percentage of women are not allowed to join this branch of the military because of their height OB Yes because the percentage of women who meet the height requirement is fairly large C No because only a small percentage of women are not allowed to join this branch of the military because of their height OD No because the percentage of women who meet the height requirement is fairly small b For the new height requirements this branch of the military requires women s heights to be at least most in Round to one decimal place as needed in and at

Calculus

Vector CalculusPlot the vector field F ri y j Now consider the points P 1 5 0 5 and P 1 5 0 5 Identify whether these points are sources or sinks Using the definition of divergence verify your answer

Calculus

Definite IntegralsFind the indefinite integral Use C for the constant of integration Jar arcsec 3x dx x x arcsec 3x 1 w r In 9x 1 3x 2 3 C

Calculus

Limits & ContinuityProblem 1 Use an appropriate test to determine whether the series converges Ek 1 COS 14

Calculus

Vector CalculusConsider the following equations 2 2y 4x 3 x y and y 5 6 7x Step 1 of 3 Express the first equation in slope intercept form Simplify your answer Anguo

Calculus

Application of derivativesIn this last step we are going to go back to our first reflection We asked the question Are vertical stretches shrinks and horizontal stretches shrinks basically the same thing Yes that s right we re asking the first question again This time apply the following sequence of transformations to your chosen function f x Graph Transformations f x x2 The vertical stretch by 4 then a vertical shift by 2 A horizontal shrink by 2 and then a vertical shift by 2 A vertical shift by 2 then a vertical stretch by 4 A vertical shift by 2 then a horizontal shrink by 2