Limits & Continuity Questions and Answers

No calculators Find the exact length of the curve Only use methods taught In lecture Show full work justify fully y 2 2x 2 0 x 1

Confirm that the Integral Test can be applied to the series Then use the Integral Test to determine the convergence or divergence of the series In n 8 8 n 1 In x dx converges diverges 1 49

Question The function f x x 2x 7 is Select O N 2 3

Evaluate the integral 5 1 ds 5 2 s 5 25 ds

4hom Use the graph of the function to answer each part Some choices may be used more than once 14 7 State the domain of the function For what value s of x does f x 3 State the range of the function Evaluate f x for x 3 1 0 00 2 00 3 U 3 00 3 00 3 U 3 00 4 0 3 U 3 00 5 Undefined or does not exist 6 3 7 3

If the acceleration A t of an object is proportional to the square root of its speed S t write the differential equation for the acceleration of the object Do not solve o A t S dt o A t ds k o A t k S dS o A t d KS 83 84 85 86 87 88 89 90 91 92 Mont

A personal computer salesperson receives a base salary of 2000 per month and a commission of 5 of all sales over 10 000 during the month If the monthly sales are 20 000 or more then the salesperson is given an additional 700 bonus Let E s represent the person s earnings per month as a function of the monthly sales s Answer parts a through d a Graph E s for 0 s 30 000 Choose the correct graph below OA AE S 5000 0 OA 0 b Find 41 S 30 000 lim E s s 10 000 OB The limit lim OB s 10 000 AE s 5000 E s does not exist 0 0 30 000 G O C AE s 5000 lim E s Select the correct choice below and if necessary fill in the answer box to complete your choice S 10 000 0 0 30 000 Q D AE S 5000 0 0 30 000 Q

5 You are starting a sock company You must determine your costs to manufacture your product The start up cost is 2000 which helps you purchase sewing machines Material and labor is 2 50 per pair of socks a Write an equation to model your company s cost for manufacturing the socks i e y mx b b Which variable represents the domain Explain your answer c What is the domain for this situation d Which variable represents the range Explain your answer e What is the range for this situation f Using your equation what would be the cost of manufacturing 25 pairs of socks g How many socks could you make with 2500 h Create a coordinate graph on a sheet of paper to represent this situation Describe the graph Include the

5 Assume that the 2 2 matrix A has one eigenvalue X only so that A AI 0 Show explicity that x e t I t A XI v is the general solution of x Ax

The table below gives the power consumption P in megawatts in a county from midnight to 6 00 a m on a day in December Use Simpson s rule to estimate the energy used during that time period Use the fact that power is the derivative of energy Round your answer to one decimal place t 0 00 P t P 1 814 3 30 1 619 0 30 1 737 4 00 1 625 1 00 1 684 4 30 1 668 1 30 1 642 5 00 1 743 2 00 1 635 5 30 1 886

What are the domains and ranges of the following functions Function y cos x y tanx y CSCx Domain Range Domain Range Domain Choose one The set of all real numbers except integer multiples of TC The set of all real numbers except odd integer multiples of 2 The set of all real numbers from 1 to 1 The set of all real numbers The set of all real numbers less than or equal to 1 or greater than or equal to 1

Draw the graph of f x Provide your answer below 2 7 S y 5 0 4 1

The graph of an exponential function passes through 1 10 and 4 80 Find the function that describes the graph Provide your answer below

Click here to view the transcript ou cannot take the sum of an infinite geometric series Assume that 1 r 1 in the video True False

Find the sum of the convergent series 3 2 8 8 6 3 32

Determine whether or not the function f x 6 3x 3 is continuous everywhere If it is continuous everywhere it is defined enter the domain on which it is continuous interval notation To enter type infinity To enter U type U If it is discontinuous state where it is discontinuous Enter your answer as a list numbers separated by semicolons e g 2 4 6 The order of the list does not matter

lim 1 3 0 0 1 cos ry 8 y e DNE for does not exist oo for infinity or oo for negative infinity Evaluate

Find the function value if possible If an answer is undefined enter UNDEFINED h t t2 t 1Find the function value if possible If an answer is undefined enter UNDEFINED h t t 1 h 3 h 1 h x 1

Find the x values if any at which fis not continuous If there are discontinuities determine whether they are removable Enter your answers as comma separated lists If an answer does not exist enter DNE f x 7 csc TX 14 removable discontinuities nonremovable discontinuities x 3 2 x 3 2 X

Find the domain of the function using inequality notation f x 6 x 4

1 point Let f be defined by x 2 Ax B x 1 1 x 6 2x 7 6 x Find the values of A and B which make f continuous everywhere A B f x JUS help numbers

15 Find the limit x y 24 lim Y 0 O 1 1 D D

Let P x and Q x be Polynomials Find lim POD if the degree of P X 135 end X6 QQ the degree of 20x 13 9 9

Evaluare the limit lim 1 1 x X 70 X 00 2 6 22

A 14 limit cquals 1 6 For what value of the constant cis the function of continuous on 200 00 F x x 7 C 1 c 2 for x 2 Z x 5 for x 2

Is there a number a such that lim X 3 If so find the value of a and the value of the limit Select the correct answer 6x ax a 2 exists x x 6 2 14 limit equals 1 4 6 2 17 limit equal 1 6 2 28 limit cquels 1 4 2 28 limit cquals 1 6 a 14 limit equals 1 6

Which of the following statements about the function f if true cannot be used to conclude that fis defined at x 1 f is continuas at x 1 Tre line tangent to the graph of f at x 1 exist S The limfax exists X A fis differentiable at x 1

lim 2 3y2 54 44 Y D 1 1 20 viin min b 3

How would you define f 4 in order to make of continuous at 4 f x x x 12 X 4

A motorcycle travels 20 miles west and then turns and goes 52 north of west another 38 miles How far is the motorcycle from its starting point miles Round to the nearest tenth

A trough is 3 meters long 3 meters wide and 3 meters deep The vertical cross section of the trough parallel to an end is shaped like an isoceles triangle with height 3 meters and base on top of length 3 meters The trough is full of water density 1000 kg Find the amount of work in m joules required to empty the trough by pumping the water over the top Note Use g 9 8 as the acceleration due to gravity 8 PRO m

You self publish a book and desire to get it printed The printer tells you that the average cost per book is 120 4x C x where x is the number of books printed Directions Answer the following questions a post For full credit create your post and view and respond to two of your classmates 1 What is the approximate cost per book when 50 books are printed 100 books 2 You plan to charge 8 per book About how many should be printed to make a profit solve algebraically 3 Give an explanation of what you think the meaning of the value of 120 is in the function 4 What does the end behavior of the function say in the context of this situation

6 In Harry Potter and the Deathly Hallows Harry Ron and Hermione use the Polyjuice Potion to change their appearance in order to get the Slytherin locket from Dolores Umbridge at the Ministry of Magic The potion loses 18 of its effectiveness every 15 minutes Determine the half life of the potion to the nearest minute 4 marks otion loses its effectiveness when there is less than 15 of the potion in the body How much time minuta 4 marks

3 Given log54 whole numbers 5 marks 27 2000 in terms of x y and or x and log53 y determine an expression for logs 2000

UT 2 T 3 Given log54 x and log53 y determine an expression for logs whole numbers 5 marks 2TT 4 T 27 2000 in terms of x y and or

The graph of the rational function f x is shown below Using the graph determine which of the following local and end behaviors are correct Select all correct answers Select all that apply E As x f x 1 As x 2 f x As x 2 f x As x f x 1 As x 2 f x As x f x 1 3

Find lim 2 1 22 x 4 7 4 2 4 X 4 y 4 P 5 2 2 2 2 lim P 5 2 2 3 4 7 4 2 1 0 X 4 Z 4 Type an integer or a simplified fraction

x 5 f x 7 x 3 if 4sx 1 if x 1 if x 1 a Find the domain of the function The domain of the function f is Type your answer in interval notation b Locate any intercepts Select the correct choice below and if necessary fill in the answer box to complete your choice A The intercept s is are Type an ordered pair Use a comma to separate answers as needed OB There are no intercepts c Graph the function Choose the correct graph below O A OB Q Q O C d Based on the graph find the range Select the correct choice below and fill in the answer box es to complete your choice OA The range has at least one isolated value It can be described as the union of the interval s and the set O D

Find lim x y 0 0 w 3e sin 2x 5x 3e sin 2x lim 5x x y 0 0 Type an exact answer 11

Find the limit If an answer does not exist enter DNE lim 5 www 6ur 8 x 5

Sketch the region enclosed by y 3x and y 7x Find the area of the region I Question Help Video Message instructor

a Find the following limits If an answer does not exist enter DNE F x Em F x b 3 x l x 2 x21 Does lim f x exist 8 1 O Yes ONO PUN 2 3 c Sketch the graph of f no 1 DO DO

Example 2x 3 x 3x 5 4 c m 7n 2x x 2x 3 x 3x 3x 2x 3x 3 3x muni 6x 3 Answer 2x 3 x 3x 5 3x 19x 15 7 Perform the indicated operations and simplify the results a 4x x 1 x x 2 b x 3 x 10x 2x 5 3 5 15 d x h 2 x h 5

12 30 points Let f x F x and h x be defined as the following e 1 A 2 f x TX F x f f t dt h x a 15 points Find limo h x b 15 points Find limx o h x f x 1 F x

Find the area of the trapezoid shown below 8 7 1 19 5 M 3 CH M Area 1 4 7 8 9 1 Question Help Video Message instructor Calculator

Find the value of cos 20 if e is in the third quadrant and sin 0 1 33 12

The distance formula d rt where d distance traveled The simple interest formula I Prt where Total cost r rate t time interest P amount borrowed invested T interest rate t time C pq where T C total costs p price per unit g quantity Coin Value Name Value Value 3 A car was traveling at a rate of x miles per hour for 3 hours How far did the car travel 4 You invest x dollars at 5 percent annual rate for 2 year How much is the simple interest 5 You bought y pounds of apples at 1 75 per pound How much did you pay for the apples 6 You have x dimes and y nickels in your pocket In all how many coins were in your

A sine function has an amplitude of 2 period of 8 horizontal shift of and vertical shift of 1 What is the y value of the positive function at x 4 y Enter

Give the complex number of point B yi B 6543 22 1 C 56 A 7 6 5 4 3 2 11 1 2 3 4 5 6 2 3 4 5

Find the volume of the parallelepiped with adjacent edges PQ PR and PS P 2 0 3 Q 4 1 8 R 5 3 1 S 1 4 4 cubic units