# Calculus Questions

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Differentiation
6 Use Logarithmic Differentiation to differentiate to find dy dx given 3 x x 1 x 2 x 1 2x 3 y Calculus
Differentiation
Let 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 Integration
Graph 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 Integrals
How 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 derivatives
3 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 Integrals
Use 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 Integrals
Use Simpson s rule with n 6 to approximate cos z dz Keen at least 2 decimal places accuracy in your final answer Calculus
Definite Integrals
The 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 Integrals
Use the Midpoint Rule with n 3 to approximate the integral 2x 102 da Calculus
Vector Calculus
Use the Midpoint Rule with n 6 to approximate th T dr Calculus
Definite Integrals
A 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 & Continuity
What 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 Calculus
Consider 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 Integrals
Which 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 Integrals
What 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
Definite Integrals
Evaluate O 24 O 30 O 36 O 42 2x 7 dx 25 26 27 28 29 Calculus
Application of derivatives
points 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 Integration
Which 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 equations
For 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 Integration
Rewrite 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 Integration
Which 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 Integration
Consider 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
Indefinite Integration
x 3 dx x What is F x O F x x 3 C O F x x 3 C F x x 3 c C F x x 3 Calculus
Definite Integrals
What 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 Integrals
Find 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 & Continuity
What is the smallest angle of this triangle 12 23 34 Round to the nearest hundredth Ente Calculus
Vector Calculus
OSCAGC03s02q512P 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 Integration
For 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 & Continuity
Calculate the exact value of sin 67 using the half angle formula Rationalize the denominator if necessary sin 67 5 Enter or Ent Calculus
Limits & Continuity
Given 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
Differentiation
the 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 Integrals
A 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
Vector Calculus
Find a complex vector d so that if F fo f1 2 3 f2 F 0 fi f2 0 c then F Calculus
Indefinite Integration
An 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 Integrals
Rewrite 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
Differentiation
Which 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 derivatives
Find 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 & Continuity
Find 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 Integrals
An 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 Calculus
What 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 Integration
Consider 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 Integrals
Rewrite 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 derivatives
Find the area of this triangle 155 260 175 Round to the nearest whole number Calculus
Application of derivatives
0 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 Calculus
Plot 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 Integrals
Find 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
Application of derivatives
find the derivative of the function F x In CSX 2 5x 2 Calculus
Limits & Continuity
Problem 1 Use an appropriate test to determine whether the series converges Ek 1 COS 14 Calculus
Vector Calculus
Consider 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 derivatives
In 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