Limits & Continuity Questions and Answers

Describe the end behavior of the function f x 3x 4x 19 by finding lim f x and lim f X X lim f x Simplify your answer X 8 lim f x Simplify your answer

Find each function value and the limit for f x A f 10 A f 10 Round to the nearest thousandth as needed OA lim B f 20 8118 10 7x 6 x 10 7x 6 x B f 20 Round to the nearest thousandth as needed C Select the correct choice below and if necessary fill in the answer box to complete your choice Use o or o where appropriate C lim f x 8118

The graph of y f x is shown in the figure above If A and dy are positive numbers that represent the areas of the shaded regions then in terms of 4 and 4 f x dx 2 f x dx A 4 B 4 4 OA OB Oc C OD 4 C 24 4 D A A E 4 24

144 12 Hours The flow of oil in barrels per hour through a pipeline on July 9 is given by the graph shown above Of the following which best approximates the total number of barrels of oil that passed through the pipeline that day A 500 B 600 OA OB Oc OD Barrels per Hour 200 100 O 6 C 2 400 18 24 D 3 000 E 4 800

Find x where 0 x 2 4 2 tan x 2 3 2 tan x T 7 Enter the smallest answer first Enter

A Find tan 15 2 3 C 3 2 D 2 3 2 3

y 3 y 5 Determine the interval over which h is continuous and the interval over which h is differentiable Consider h y h is continuous on h is differentiable on Part 1 of on 9 6

15 polata total 13 Answer the following questions for the graph shown below The xsdl and the yscla 5 1 pott a Amplitude 2 posts b Period 10 points d Determine anytrigonometric function whose graph is identical to the one shown Show all work Equation 2 pos c range 9152 18 12 M 112

etermine g x a g x for the following function Answer g x 5x 4x

Triangle ABC in the grid is reflected across x axis and then across y axis Identify the vertices of the triangle after transformation

0 Let f x A alx x 21 2 x x b X X 2 X 2 X 2 X 2 denotes the greatest integer function If f x is continuous at x 2 then a 1 b 2 B a 1 b 1 C a 0 b 1 D a 2

Given that f lim f x 1 X13 Jim g x lim h x 0 find each limit if it exists If an answer does not exist enter DNE a lim f x 5g x b lim g x 3 e c lim f x x 3 d lim 2f x x 3 g x lim 9 x x 3 h x g x h x 2 lim X 3 f x

Use the graph of the function f shown in the figure to the right to estimate the indicated function value f 1 9

3 Find a sin300 d sec 315 4 Convert b cos 120 e sec 90 a 5 radians to degrees 5 b to radians c 3 radians to degree d 3 to radians 5 T e 12 radians to degrees f 90r to radians g 1or to radians 1 h 3radians to degrees c tan480 f CSc 210

Find the nth term of a sequence Click here to view the transcript To find the nth term of a given sequence with alternating signs introduce the factor 1 or 1 n 1 O True

an Determine the convergence or divergence of the sequence with the given nth term If the sequence converges find its limit If the quantity diverges enter DIVERGES 6 n

Listen Evaluate the following limit if it exists 1K 1A 2 3x 2 x 1 lim 1

By the alternating series test the series 3 k k 4 3 4k First find the partial fraction decomposition of 3 4k16 L 8 Or k 1 3 1 1 k k 4 3 k k 4 Then find the limit of the partial sums 3 1 k 1 k k 4 k 1 Enter your answer for the sum as a reduced fraction converges Find its sum Hint The alternating series is a telescoping series Write down its terms using the partial fractio decomposition until some terms cancel

x 0 15x 0 025xy y 0 25y 0 025xy a Find the critical point in the first quadrant x y 10 6 Use a numerical solver to sketch some population cycles Choose x 0 9 and y 0 5 14 14 12FX t 10 O 8 6 4 2 14 Fy t 12 x t 10 8 6 4 20 ty t x 20 40 60 40 80 60 t t 80 100 12 EX t 100 10 8 12 FX t 10 ma 8 6 4 y t 2 O 6 4 0 ty t 0 14 20 40 20 60 40 80 60 t 80 100 t 100 b Estimate the period of the periodic solutions that are close to the critical point in part a Choose x 0 9 and y 0 5 Use a CAS to estimate the period and round your answer to two

2 14 pts Given that sino and is in the third quadrant find the other function valu 3 16pts Find a cos 720 b tan 5 c sin 240 d sec

6 18 pts Evaluate the following a sin 1 b tan 3 c cos

4 16 pts Convert each of the following to a 12 degree to radian b rad to degrees 5 20 pts Graph one cycle of the graph of f Label the high low points Show all steps in transformation f x 3sin 2x 3

Divide 60x4 32x3 37x223x 3 by 6x 1

The total number of people that visit local coffee shops in one area can be modeled by the function f x 63x 37x 77x 65 where x is the number of years passed since 1990 The number of local coffee shops can be modeled as f x 9x 5 Use division to find an expression that can be used to determine the average number of people that visit the local coffee shops

Divide 6x 5x 3 2x 5 Write your answer in the following form Quotient 3 6x 5x 3 2x 5 1 2 2x 5 2 Remainder 2x 5

Suppose is an angle such that cos 0 If 0 2 then cos 0 2 and sin 0 9 2 4 NIN 2

100000 80000 60000 40000 20000 y2 000 40 000 4 8 00 10 60000 12 16 20 Year A Year 10 12 14 16 18 20 22 Earnings dollars 55 000 60 000 65 000 70 000 75 000 80 000 85 000 When will Janis s salary be the same for job 1 and job 2 and how much will she be earning at that point O The salaries will be the same in year 20 and she will be earning 80 000 The salaries will be the same in year 16 and she will be earning 70 000 The salaries will be the same in year 12 and she will be earning 60 000 O The salaries will be the same in year 10 and she will be earning 55 000 Submit

Divide 60x 40x 54x 38 by 6x 4 Report your answer as a quotient plus fractional remainder if necessary e

Graph the feasible region for the system of inequalities y 4x 1 y 2x 3 Use the graphing tool on the right to graph the feasible region for the system of inequalities 10 2 104 8 6 4 2 42 4 4 164

For the piecewise function find the values h 9 h 7 h 4 and h 9 4x 18 for x 8 h x 4 x 1 h 9 for 8 x 4 for x 4

Sketch the region enclosed by the given curves y 2 0 y 3 y cos x y 2 cos x 0 x 2 KIN KIN 2 3x 2 3A 2 2x 2x y 3 2 1 2 R 1 2x 1 00 2 7 3 T 2 2A

Step 4 Using y t 110ekt and the fact that y 30 75 we can solve for k y t 110ekt 75 y 30 540 75 540 15 22 k 30 110e k 110e Thus we have the following equation 22 1 k In 30 3 15 x Thus we have the following T 70 y 70 75 30 1 30 Step 5 Substituting the value of k found above we have y t 110e 1 30 tin 15 22 Now substitute for t 70 to find the temperature of the turkey after 70 minutes Round you answer to the nearest whole number y 70 110e 1 30 70 In 15 22 X 75 In 30 30

portion of the plane 3x 2z 6 Choose the correct graph of the plane OA OB SIID O C

2 You work in a hospital and are in charge of a patient with rheumatic fever At the beginning of your shift you record the patient s temperature at 99 9 In ten minut you return and record his temperature to be 100 7 After 2 hours his temperature has now risen to 102 4 a Calculate the slope and y intercept of the equation modeling this situation Explain the meaning of the slope in context of this situation What does the y interc represent b On graph paper graph the line Using the graph and your equation determine the patient s temperature 30 minutes 1 hour and 90 minutes after the beginning shift You do not need to submit your graph c You need to predict what his temperature will be 4 hours later Explain your result Is it reasonable d What does the domain represent in this situation e What does the range represent in this situation f Should the domain have any restrictions or can it go to infinity g Should the range have any restrictions or can it go to infinity

Substituting the value of k found above we have y t 110e 1 30 tin 15 22 Now substitute for t 70 to find the temperature of the turkey after 70 minutes Round your answer to the nearest whole number y 70 110e 1 30 70 In 15 22 X Thus we have the following T 70 y 70 75 R B X 75 X F

The graph of the derivative fof a function is shown 10 12 14 a On what interval is f increasing Enter your answer using interval notation On what intervals is f decreasing Enter your answer using interval notation b At what values of x does Fhave a local maximum or minimum Enter your answers as a comma separated list

Find the complex number associated with the point shown on the graph What is the complex number associated with the point OA 3 4i OB 3 4i OC 3 4i OD 3 4i

6 x 4 The interval is Type your answer in interval notation Choose the correct graph below OA 10 2 POB 10 10 2

Solve by completing the square 14x 10 The solution set is Type an exact answer using radicals as needed U as needed

Consider the following inequality problem 6w7w 6 or 1 5w 51 Step 1 of 4 Solve the first inequality and express your answer in interval notation Use decimal form for numerical values Answer Answered 2 Points Lim oluf6cll Keyboar

Find the domain of the function and identify any horizontal and vertical asymptotes Enter the domain in interval notation Enter NONE if there is no asymptote f x 1 5x 1 4x domain vertical asymptote horizontal asymptote X y

cx 6x 6x Let f x 9 x cx if x 3 if x 3 For what value of the constant c is the function of continuous on co C 0 75

Find the pivot in the simplex table 14 X1 232 X2 S1 S2 Z 2 0 1 0 4 1 0 0 3 8

Decide whether the statement is true or false 18 2 SO 2 31 C

The graphs of which functions approach positive infinity as x approaches both negative infinity and positive infinity Selec all that apply Select all that apply Of x x 5x 9 Of x 4x 5x Of x 19x4 8x 1 f x 9x5 4x4 3x 8 f x 18x5 8x 6 Of x 3x 7x4 9x CUDI

As x approaches infinity for which of the following functions does f x also approach infinity Select all that apply f x 6x4 f x 18x 2 f x 4x5 16x 10 f x 6x 4x 18x f x 7x4 19x 18x 11 f x 2x6 3x5 18x3 12x 5

Determine the value of each variable in the matrix equation 2x 3 3y 4 7 10 17 37 7 18

LINE A LINE A LINE C Use the magenta graph above to answer the following questions Does the graph pass the vertical line test for Line A yes no How many times does Line A intersect the graph 0 1 2 3 Does the graph pass the vertical line test for Line B yes no How many times does Line B intersect the graph 0 1 2 3 Does the graph pass the vertical line test for Line C yes no How many times does Line C intersect the graph 0 1 2 3 Applying the vertical line test for functions does this graph represent at function

Recall the following special limit where c is a constant lim c c x 00 Applying the above gives us the following lim 8 lim X18 X 8 lim 5 lim x18 X18 7 2 lim X18 3 7 2 lim X 8 3 Jim lim 2 X 8

Find lim x y 0 0 5e sin 4x 4x 5e sin 4x lim 4x x y 0 0 Type an exact answer 11