Limits & Continuity Questions and Answers
![Find the roots of the equation z 27i 0 in the form a bi](https://media.kunduz.com/media/sug-question-candidate/20230210045232837430-4827739.jpg?w=256)
![2 1 The slope of the tangent line to the curve y at the point 8 X is The equation of this tangent line can be written in the form y mx b where m is b is](https://media.kunduz.com/media/sug-question-candidate/20230210023431446730-4565383.jpg?w=256)
Calculus
Limits & Continuity2 1 The slope of the tangent line to the curve y at the point 8 X is The equation of this tangent line can be written in the form y mx b where m is b is
![Consider the following 0 cos 3 Find the length of the third side of the triangle in terms of x e tan X Find in terms of x for all three inverse trigonometric functions e sin](https://media.kunduz.com/media/sug-question-candidate/20230210014615229736-3899453.jpg?w=256)
Calculus
Limits & ContinuityConsider the following 0 cos 3 Find the length of the third side of the triangle in terms of x e tan X Find in terms of x for all three inverse trigonometric functions e sin
![Equation Given two points x y and x2 y2 the equation for the line that passes through these two 1 1 x X X 0 y V V2 Use this determinant to find the equation for the line that passes through the points 2 7 and 4 4 Write the final answer in slope intercept form 8 pts points is given by a](https://media.kunduz.com/media/sug-question-candidate/20230210010507746315-4709559.jpg?w=256)
Calculus
Limits & ContinuityEquation Given two points x y and x2 y2 the equation for the line that passes through these two 1 1 x X X 0 y V V2 Use this determinant to find the equation for the line that passes through the points 2 7 and 4 4 Write the final answer in slope intercept form 8 pts points is given by a
![Find the difference quotient Find f 0 Find f x by determining lim h 0 Find f 2 This slope should match the tangent line you drew above Clear Al DEBULL Find f 1 Graph the function f x 2x and draw the tangent lines to the graph at points whose x coordinates are 2 0 and 1 10 9 8 7 f x h f x h 6 5 3 f x h f x h 4x 2h](https://media.kunduz.com/media/sug-question-candidate/20230210005900364548-4565383.jpg?w=256)
Calculus
Limits & ContinuityFind the difference quotient Find f 0 Find f x by determining lim h 0 Find f 2 This slope should match the tangent line you drew above Clear Al DEBULL Find f 1 Graph the function f x 2x and draw the tangent lines to the graph at points whose x coordinates are 2 0 and 1 10 9 8 7 f x h f x h 6 5 3 f x h f x h 4x 2h
![11 4 2 0 0 1 the matrix product AB defined Let A 0 2 B 1 1 1 3 3 3 D B 3 2 5 3 2 2 DB 1 2 3 B 2 For which of the following matrices is](https://media.kunduz.com/media/sug-question-candidate/20230209211921452781-5281911.jpg?w=256)
Calculus
Limits & Continuity11 4 2 0 0 1 the matrix product AB defined Let A 0 2 B 1 1 1 3 3 3 D B 3 2 5 3 2 2 DB 1 2 3 B 2 For which of the following matrices is
![6 8 1 4 0 2 1 1 3 following matrices is equal to the linear combination A 3B Let A 9 1 329 O 123 7 9 O 8 4 13 3 0 1 4 and B Which of the](https://media.kunduz.com/media/sug-question-candidate/20230209211902772385-5281911.jpg?w=256)
Calculus
Limits & Continuity6 8 1 4 0 2 1 1 3 following matrices is equal to the linear combination A 3B Let A 9 1 329 O 123 7 9 O 8 4 13 3 0 1 4 and B Which of the
![Complete the following questions a b 24 is 5 of 5 of what amount is 6 00 Answer](https://media.kunduz.com/media/sug-question-candidate/20230209200646283893-4754718.jpg?w=256)
Calculus
Limits & ContinuityComplete the following questions a b 24 is 5 of 5 of what amount is 6 00 Answer
![points Save All Answers ENG US Save Save and](https://media.kunduz.com/media/sug-question-candidate/20230209200502925322-4754718.jpg?w=256)
![an A parking garage cha maximum length of tim](https://media.kunduz.com/media/sug-question-candidate/20230209164402279061-3653173.jpg?w=256)
![5 16253649648 The next seven dig](https://media.kunduz.com/media/sug-question-candidate/20230209155528467260-3653173.jpg?w=256)
![Use the graph of f in the figure to do the following a Find the values of x in the interval 0 5 at which f is not continuous b Find the values of x in the interval 0 5 at which f is not differentiable Ay 20 16 12 8 4 0 4 8 12 16 20 Q a In the interval 0 5 f is not continuous at x Use a comma to separate answers as needed b In the interval 0 5 f is not differentiable at x Use a comma to separate answers as needed](https://media.kunduz.com/media/sug-question-candidate/20230209142855479750-4726954.jpg?w=256)
Calculus
Limits & ContinuityUse the graph of f in the figure to do the following a Find the values of x in the interval 0 5 at which f is not continuous b Find the values of x in the interval 0 5 at which f is not differentiable Ay 20 16 12 8 4 0 4 8 12 16 20 Q a In the interval 0 5 f is not continuous at x Use a comma to separate answers as needed b In the interval 0 5 f is not differentiable at x Use a comma to separate answers as needed
![ometimes even when we are not sure whether or not a particular limit exists we can still use algebra t now that there are only a small number of possible values the limit could take a Last week in tutorial we saw that lim tan sin It also happens to be true though we will no x 0 x3 3 verify it at this time that lim tan x 2 Suppose that lim sin exists Determine the value sin the limit Hint This is a special case of part b x 0 b Suppose f x g x and h x are three functions with lim f x xc g x f x i If M 1 show that either lim ii What can you say if M 1 M and lim f x g x h x X C ML 1 M or the limit does not exist L](https://media.kunduz.com/media/sug-question-candidate/20230209133031643858-5369347.jpg?w=256)
Calculus
Limits & Continuityometimes even when we are not sure whether or not a particular limit exists we can still use algebra t now that there are only a small number of possible values the limit could take a Last week in tutorial we saw that lim tan sin It also happens to be true though we will no x 0 x3 3 verify it at this time that lim tan x 2 Suppose that lim sin exists Determine the value sin the limit Hint This is a special case of part b x 0 b Suppose f x g x and h x are three functions with lim f x xc g x f x i If M 1 show that either lim ii What can you say if M 1 M and lim f x g x h x X C ML 1 M or the limit does not exist L
![Write the standard form of the equation and the gene Then graph the circle r 5 hk 3 4](https://media.kunduz.com/media/sug-question-candidate/20230209073147362043-5066220.jpg?w=256)
Calculus
Limits & ContinuityWrite the standard form of the equation and the gene Then graph the circle r 5 hk 3 4
![22 tan 52 tan 57 12 1 tan 51A 2 tan 7 1 7 and cost 1 13 45 055 sandt in quadrant](https://media.kunduz.com/media/sug-question-candidate/20230209063545975385-4412862.jpg?w=256)
Calculus
Limits & Continuity22 tan 52 tan 57 12 1 tan 51A 2 tan 7 1 7 and cost 1 13 45 055 sandt in quadrant
![In Sarah s community the Primary school bell rings every 30 minutes and the High school rings every 40 minutes Both schools start at 8 00am Determine at what time the bells ring at the same time between 8 30 am and 11 am Show all possible calculations 5](https://media.kunduz.com/media/sug-question-candidate/20230209061505341414-5369415.jpg?w=256)
Calculus
Limits & ContinuityIn Sarah s community the Primary school bell rings every 30 minutes and the High school rings every 40 minutes Both schools start at 8 00am Determine at what time the bells ring at the same time between 8 30 am and 11 am Show all possible calculations 5
![K What is the shading style of the for The forty first figure in the sequenc](https://media.kunduz.com/media/sug-question-candidate/20230209043317215439-3653173.jpg?w=256)
Calculus
Limits & ContinuityK What is the shading style of the for The forty first figure in the sequenc
![Which option describes the end behavior of the function f x 5 x 6 x 3 3x 2](https://media.kunduz.com/media/sug-question-candidate/20230209041506151116-5369300.jpg?w=256)
Calculus
Limits & ContinuityWhich option describes the end behavior of the function f x 5 x 6 x 3 3x 2
![K Ty CM 3 32 Part 1 of 5 Fill in the reason that justifies each step ZCDE and ZEDF are supplementary mZCDE mZEDF 180 x 4x 20 180 5x20 180 5x 200 x 40 4 that form supplemen a b c d e](https://media.kunduz.com/media/sug-question-candidate/20230209022524819635-3653173.jpg?w=256)
Calculus
Limits & ContinuityK Ty CM 3 32 Part 1 of 5 Fill in the reason that justifies each step ZCDE and ZEDF are supplementary mZCDE mZEDF 180 x 4x 20 180 5x20 180 5x 200 x 40 4 that form supplemen a b c d e
![Find the interval of convergence for x 2 n 2 n 1](https://media.kunduz.com/media/sug-question-candidate/20230208234413911504-4044772.jpg?w=256)
![Find each of the following functions f x 5 x g x x 4 a f g State the domain of the function Enter your answer using interval notation b f g State the domain of the function Enter your answer using interval notation c fg State the domain of the function Enter your answer using interval notation d f g State the domain of the function Enter your answer using interval notation](https://media.kunduz.com/media/sug-question-candidate/20230208173719488316-4768444.jpg?w=256)
Calculus
Limits & ContinuityFind each of the following functions f x 5 x g x x 4 a f g State the domain of the function Enter your answer using interval notation b f g State the domain of the function Enter your answer using interval notation c fg State the domain of the function Enter your answer using interval notation d f g State the domain of the function Enter your answer using interval notation
![7 In the diagram segment JK Gl Solve for x if HJ 3x HK 2x KI 6x and JG 18 units a x 1 b x 2 a C d C X 4 d x 5 Ge H J K](https://media.kunduz.com/media/sug-question-candidate/20230208160830545464-4946438.jpg?w=256)
Calculus
Limits & Continuity7 In the diagram segment JK Gl Solve for x if HJ 3x HK 2x KI 6x and JG 18 units a x 1 b x 2 a C d C X 4 d x 5 Ge H J K
![Solve the eq 5x 4y The solution](https://media.kunduz.com/media/sug-question-candidate/20230208155918101559-3653173.jpg?w=256)
![Solve the compound set of the compound 5x 30 inequality solution ine 3x 6 and](https://media.kunduz.com/media/sug-question-candidate/20230208152421171882-5367895.jpg?w=256)
Calculus
Limits & ContinuitySolve the compound set of the compound 5x 30 inequality solution ine 3x 6 and
![Find the frost 5 terms a n 1 n 1 b d An n 1 1 n 1 3n an n 3 n 3 cos TT 6 n 0](https://media.kunduz.com/media/sug-question-candidate/20230208125004426851-5367846.jpg?w=256)
Calculus
Limits & ContinuityFind the frost 5 terms a n 1 n 1 b d An n 1 1 n 1 3n an n 3 n 3 cos TT 6 n 0
![The following are the cash flows of two projects Year Project A 0 81234 1 2 3 4 330 160 160 160 160 Project B 330 230 Project A B If the opportunity cost of capital is 12 what is the profitability index for each project Note Do not round intermediate calculations Round your answers to 4 decimal place 230 230 Profitability Index](https://media.kunduz.com/media/sug-question-candidate/20230208072125645819-4407255.jpg?w=256)
Calculus
Limits & ContinuityThe following are the cash flows of two projects Year Project A 0 81234 1 2 3 4 330 160 160 160 160 Project B 330 230 Project A B If the opportunity cost of capital is 12 what is the profitability index for each project Note Do not round intermediate calculations Round your answers to 4 decimal place 230 230 Profitability Index
![Use the formula to f A bh find A when answer is A](https://media.kunduz.com/media/sug-question-candidate/20230208074731634736-3653173.jpg?w=256)
![and Solve the equation 3 9x 3 2 8 5 Que](https://media.kunduz.com/media/sug-question-candidate/20230208061807225692-3653173.jpg?w=256)
![and Operations Equations K Solve the equation 1 X 3 9 9 3](https://media.kunduz.com/media/sug-question-candidate/20230208051628896352-3653173.jpg?w=256)
![14 10 points Let 0 0 0 5 0 2 3 and B I A IA Find I B A 10 2 3 0 4 0 1 I 1000 0 1 0 0 0010 0 0 0 1](https://media.kunduz.com/media/sug-question-candidate/20230208045739704151-5366935.jpg?w=256)
Calculus
Limits & Continuity14 10 points Let 0 0 0 5 0 2 3 and B I A IA Find I B A 10 2 3 0 4 0 1 I 1000 0 1 0 0 0010 0 0 0 1
![Domain Range 6 Domain Range X O 49 Function y 2345 YTON of Domain Range Function 8](https://media.kunduz.com/media/sug-question-candidate/20230208051153990282-4902802.jpg?w=256)
Calculus
Limits & ContinuityDomain Range 6 Domain Range X O 49 Function y 2345 YTON of Domain Range Function 8
![Solve the equation 4 4n 3 2 3n 8](https://media.kunduz.com/media/sug-question-candidate/20230208045648006195-3653173.jpg?w=256)
![Explain your answers in words 1 You are given a graph how do you use VLT Vertical Line Test to decide if the given graph represents a function 2 When a function f x is given how do you evaluate f a b](https://media.kunduz.com/media/sug-question-candidate/20230208040725849099-5366129.jpg?w=256)
Calculus
Limits & ContinuityExplain your answers in words 1 You are given a graph how do you use VLT Vertical Line Test to decide if the given graph represents a function 2 When a function f x is given how do you evaluate f a b
![can someone explain me how to do this problem also why do we multiply the First equation by 2 and not the second equation bh anything 36 Find the values of a and b that make f continuous everywhere x x 2 f x 1 4 ax 2x a b VT if x 2 bx 3 if 2 x 3 if x 3 45 2013](https://media.kunduz.com/media/sug-question-candidate/20230208033724257673-5367736.jpg?w=256)
Calculus
Limits & Continuitycan someone explain me how to do this problem also why do we multiply the First equation by 2 and not the second equation bh anything 36 Find the values of a and b that make f continuous everywhere x x 2 f x 1 4 ax 2x a b VT if x 2 bx 3 if 2 x 3 if x 3 45 2013
![Fill in each matrix for diagonalization of the matrix A A PDP 1 5 Ex 5 2 1 1 6 10 2 3 1](https://media.kunduz.com/media/sug-question-candidate/20230208025212012941-5366902.jpg?w=256)
Calculus
Limits & ContinuityFill in each matrix for diagonalization of the matrix A A PDP 1 5 Ex 5 2 1 1 6 10 2 3 1
![valuate the function at the given numbers correct to six decimal places X 8 1 8 05 8 01 8 005 8 001 x 7x8 x 8x X 7 9 7 95 7 99 7 995 7 999 x 7x 8 x 8x uess the value of the limit if it exists Round your answer to three decimal places If an answer does not exist x 7x8](https://media.kunduz.com/media/sug-question-candidate/20230208005340088855-5366902.jpg?w=256)
Calculus
Limits & Continuityvaluate the function at the given numbers correct to six decimal places X 8 1 8 05 8 01 8 005 8 001 x 7x8 x 8x X 7 9 7 95 7 99 7 995 7 999 x 7x 8 x 8x uess the value of the limit if it exists Round your answer to three decimal places If an answer does not exist x 7x8
![Graph the function and its inverse Include the domain restrictions 17 f x x 2 D D](https://media.kunduz.com/media/sug-question-candidate/20230207225530942534-5366951.jpg?w=256)
Calculus
Limits & ContinuityGraph the function and its inverse Include the domain restrictions 17 f x x 2 D D
![Evaluate the limit et 1 7 lim t 0](https://media.kunduz.com/media/sug-question-candidate/20230207202852815611-3819153.jpg?w=256)
![nd the limit Use l Hospital s Rule if appropriate If there is a more elementary method consider using it 9x 9 XX 1 In x X 1](https://media.kunduz.com/media/sug-question-candidate/20230207203037269574-3819153.jpg?w=256)
Calculus
Limits & Continuitynd the limit Use l Hospital s Rule if appropriate If there is a more elementary method consider using it 9x 9 XX 1 In x X 1
![Ise l Hospital s Rule to find the exact value of the lim lim 5 4 X 0 3x 2](https://media.kunduz.com/media/sug-question-candidate/20230207203110484349-3819153.jpg?w=256)
Calculus
Limits & ContinuityIse l Hospital s Rule to find the exact value of the lim lim 5 4 X 0 3x 2
![nd the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it lim sin 5x csc 7x X 0](https://media.kunduz.com/media/sug-question-candidate/20230207203009360610-3819153.jpg?w=256)
Calculus
Limits & Continuitynd the limit Use l Hospital s Rule where appropriate If there is a more elementary method consider using it lim sin 5x csc 7x X 0
![lim f x 0 lim g x 0 x a b c lim p x x a d valuate the limits below where possible If a limit is indeterminate enter INDETERMINATE a lim f x x a g x lim f x x a p x h x lim x a p x lim h x X a p x lim x a q x lim g x 0 x a 1](https://media.kunduz.com/media/sug-question-candidate/20230207202833577466-3819153.jpg?w=256)
Calculus
Limits & Continuitylim f x 0 lim g x 0 x a b c lim p x x a d valuate the limits below where possible If a limit is indeterminate enter INDETERMINATE a lim f x x a g x lim f x x a p x h x lim x a p x lim h x X a p x lim x a q x lim g x 0 x a 1
![5 Let f t te 2t and F x f f t dt a Determine F x b Use the First FTC to find a formula for F that does not involve an integra c Is F an increasing or decreasing function for a 0 Why](https://media.kunduz.com/media/sug-question-candidate/20230207191042052618-4880803.jpg?w=256)
Calculus
Limits & Continuity5 Let f t te 2t and F x f f t dt a Determine F x b Use the First FTC to find a formula for F that does not involve an integra c Is F an increasing or decreasing function for a 0 Why
![What is the value of loge 36 O 6 0 2 2 O6](https://media.kunduz.com/media/sug-question-candidate/20230207190732169995-4394539.jpg?w=256)
![Which of the following is a logarithmic function Oy log x Oy 3 Oy x 3 0 y x](https://media.kunduz.com/media/sug-question-candidate/20230207190755687980-4394539.jpg?w=256)
Calculus
Limits & ContinuityWhich of the following is a logarithmic function Oy log x Oy 3 Oy x 3 0 y x
![8 Concentrated hydrochloric acid has a density of 1 19 g mL What is the mass of 250 0 mL of HCl aq](https://media.kunduz.com/media/sug-question-candidate/20230207084038900281-4823206.jpg?w=256)
Calculus
Limits & Continuity8 Concentrated hydrochloric acid has a density of 1 19 g mL What is the mass of 250 0 mL of HCl aq
![4 taxi service charges passengers a 2 flat fee plus 0 75 per mile Which equation shows the relationship between 7 the number of miles that a passenger ravels and t the total cost of the ride](https://media.kunduz.com/media/sug-question-candidate/20230207064736688762-5366333.jpg?w=256)
Calculus
Limits & Continuity4 taxi service charges passengers a 2 flat fee plus 0 75 per mile Which equation shows the relationship between 7 the number of miles that a passenger ravels and t the total cost of the ride
![G t Complete parts a and b below a Make tables of values of G at values of 1 cos 4t 4 3 t 1 t that approach bo 1 from above and below Then estimate lim G t t 1 yo not round until the final answer Then](https://media.kunduz.com/media/sug-question-candidate/20230207051556826751-5366214.jpg?w=256)
Calculus
Limits & ContinuityG t Complete parts a and b below a Make tables of values of G at values of 1 cos 4t 4 3 t 1 t that approach bo 1 from above and below Then estimate lim G t t 1 yo not round until the final answer Then
![The graph of y f a fox 3 x 4 is shown 4 3 2 1 54 125 Fo Ne esa 55 m 4 12 O a Select each value of a for which lim f x does not exist I a 2 0 1 2 b Select each value of a for which f is not continuous at a 2 0 1 2 3 O c Select each value of a for which f is not differentiable at a 2 0 1 2 3](https://media.kunduz.com/media/sug-question-candidate/20230207035217334802-4646611.jpg?w=256)
Calculus
Limits & ContinuityThe graph of y f a fox 3 x 4 is shown 4 3 2 1 54 125 Fo Ne esa 55 m 4 12 O a Select each value of a for which lim f x does not exist I a 2 0 1 2 b Select each value of a for which f is not continuous at a 2 0 1 2 3 O c Select each value of a for which f is not differentiable at a 2 0 1 2 3
![a lim f x I 9 b lim f x I 9 c lim f x 1 9 f x x 12x 27 x315x2 27 243 help numbers](https://media.kunduz.com/media/sug-question-candidate/20230207032628006795-5366180.jpg?w=256)
Calculus
Limits & Continuitya lim f x I 9 b lim f x I 9 c lim f x 1 9 f x x 12x 27 x315x2 27 243 help numbers