# Limits & Continuity Questions and Answers

Calculus

Limits & ContinuityUse the Law of Sines to solve for all possible triangles that satisfy b 23 c 35 LB 25 conditions O ZA 119 LC 39 a 51 O ZA O ZA O ZA 117 LC 114 LC 1150 LC 40 a 55 42 a 47 40 a 49

Calculus

Limits & Continuity20 20144338 6d168319ac2e5dbf490 c0867dd8733e6 Question 42 11 09 Watch Video Graph the function f x 3 1 on the axes below You must plot the asymptote and any two points with integer coordinates Asymptote Horizontal Show Examples

Calculus

Limits & ContinuityGraph each function Lable all asymptotes lable any x y intercepts 4 x 2 22 f x A D 21 f x A B C 2 2 H B C D 3 x 2 The 4 M

Calculus

Limits & Continuity14 f x x 5 A S x x 3 B x x 5 C x 4x 4 D S x 1 x 15 g x 3 x A g x 5 Sx 25 2 3 B g x x 2 8 9 C g x x 4 2 D g x 2x 6 8

Calculus

Limits & Continuity18 x 2x 24 x 5 A x 3 9 x 5 4 B x 3 C x 3 D x 3 x 5 4 x 5 6 x 5 19 5x 30x 12 x 6 5 A 5x x 6 12 x 6 C 5x 9 x 6 9 x 6 B 5x D 5x

Calculus

Limits & ContinuityFind the inverse of each function 10 S x A x Sx B 4 C x 5 6x 5 D x 2x 6 f x 16 x 11 g x 2r 8 A g x 5 2 B g x 2 x C g x x 3 2 D g x 4 x

Calculus

Limits & ContinuityUse the formula for lowering the powers to simplify the expression a If cos 4x sin 4x cos f x then f x b If cos 4x sin 4x cos g x then g x Hint For part b use a b a b a 6

Calculus

Limits & ContinuityState the domain and range of each of the following functions Enter your answers as inequalities help inequalities Your domains should be inequalities in x and ranges in y As always type pi for T If you wish to enter type infinity a f x arccos x has Domain Range b g x arcsin x has Domain Range c h x arctan x has Domain Range

Calculus

Limits & ContinuityA high speed bullet train accelerates and decelerates at the rate of 10 ft s Its maximum cruising speed is 90 mi h Round your answers to three decimal places a What is the maximum distance the train can travel if it accelerates from rest until it reaches its cruising speed and then runs at that speed for 15 minutes mi b Suppose that the train starts from rest and must come to a complete stop in 15 minutes What is the maximum distance it can travel under these conditions mi c Find the minimum time that the train takes to travel between two consecutive stations that are 45 miles apart min d The trip from one station to the next takes at minimum 37 5 minutes How far apart are the stations mi

Calculus

Limits & ContinuityUsing the left endpoint of each subinterval in a partition of 3 subintervals each of length 3 the approximate of by the corresponding Riemann sum is O a 8010 Ob 1345 O c 38007 1 10 2014 x 4 dx O d 4257

Calculus

Limits & ContinuityUse the following graph of H to find each limit When necessary state that the limit does not exist lim H x X 2 a b lim H x X 2 c lim H x x 2 d lim H x x 1 e lim H x x r f limH x x 1 7 14 432 H 1 2 3 4 5

Calculus

Limits & ContinuityFind f a f a h and the difference quotient f a h f a where h 0 h f x 9x 1 f a P f a h f a h f a h IE

Calculus

Limits & ContinuitySolve the logarithmic equation Round your answer to three decimal places log10 x 1 8

Calculus

Limits & ContinuityFind the inverse function of f informally Verify that f f x x and f f x x f x 5 x 4 f x

Calculus

Limits & Continuityhttps www webassig Q Sketch the circle Identify its center and radius x y 2x 12y 28 0 No Solution Help 10 9 8 7 6 5 3 2 1 40 9 8 7 6 6 4 3 2 4 4 2 3 4 5 6 7 8 9 10 56 8 9 10

Calculus

Limits & ContinuityUse a graphing utility to graph the function and find any asymptotes numerically by creating a table of values for the function 6 2 02 a Graph the function f x 15 10 10 15 10 5 10 10 15 10

Calculus

Limits & ContinuityAll the necessary values have been found to calculate the margin of error We have Za 2 1 960 p 0 26 and E 0 05 Substitute these value rounding the result to four decimal places za 2 p 1 p E 1 96 2 0 26 1 0 26 n Since this value represents a sample size a whole number should be used Using the whole number smaller than this value will result in a larger than desired margin of error so the value should be rounded up to the nearest whole number Thus a sample size of should be used to ensure the margin of error of 0 05 is obtained

Calculus

Limits & ContinuityUse the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6

Calculus

Limits & Continuitydp dx The marginal price at x units of demand per week is proportional to the price p There is no weekly demand at a price of 50 per unit p 0 50 and there is a weekly demand of 8 units at the price of 23 68 per unit p 8 23 68 Use the given information to answer the questions a Find the price demand equation p x Type an exact answer in simplified fifirm Round all decimal values to the nearest hundredth as needed b At a demand of 10 units per week what is the price p 10 Round to the nearest cent as needed c Graph the price demand equation for 0 x 25 Choose the correct graph below A Ap 60 Q OB Ap 60 O C Ap 60 TTI D 60 1

Calculus

Limits & ContinuityQuestion 7 The equation y log x 5 has a vertical asymptote at X Question Help Video Message instructor

Calculus

Limits & ContinuityA company producing electric motors has established that on the average a new employee can assemble N t components per day after t days of on the job training as shown in the table below a new employee s productivity increases continuously with time on the job Use left and right sums to estimate the area under the graph of N t from t 0 to t 60 Use three subintervals of equal length for each Calculate an error bound for each estimate t N t 0 11 250 Using left sums the area is Simplify your answer 40 66 60 76 80 100 120 81 85 86 GELEB

Calculus

Limits & ContinuityA company determines that its weekly online sales S t in hundreds of dollars t weeks after online sales began can be estimated by the equation below Find the average weekly sales for the first 5 weeks after online sales began S t 6et The average weekly sales amount is Round to the nearest cent as needed

Calculus

Limits & ContinuityWhich of these graphs is the graph of y x What is its domain Graph A Graph B Q O graph D 0 00 N graph C 4 3 2 1 0 1 2 3 4 graph A 00 00 A N Graph C Q N Graph D Ay

Calculus

Limits & ContinuityWrite an inequality to describe the following set The slab bounded by the planes y 0 and y 7 planes included The inequality that describes the set of points is Simplify your answer

Calculus

Limits & ContinuitySketch the graph of a function that satisfies all of the given conditions f 0 f 2 f 4 0 f x 0 if x 0 or 2 x 4 f x 0 if 0 x 2 or x 4 f x 0 if 1 x 3 f x 0 if x 1 ora 3 2 2 6 2 4

Calculus

Limits & ContinuityThe data in the table below represents the percentage of patients who have survived after diagnosis of advanced stage breast cancer at 6 month intervals of time Time after Diagnosis years 0 5 1 1 5 2 2 5 3 3 5 Percentage Surviving 95 8 83 4 74 0 58 7 46 6 40 9 32 2 a Using a graphing utility build an exponential model from the data y 120 5681 0 6918 Type integers or decimals rounded to four decimal places as needed b Express the function found in part a in the form A t Aet where t x A t Type integers or decimals rounded to four decimal places as needed

Calculus

Limits & ContinuityAtte Sketch the region enclosed by the given curves x 9y2 x 2 7y 1 0 y 0 5 0 5 1 0 1 0 0 0 5 0 5 8 1 0 M 1 0 0 5 0 5 y 1 0 1 0 0 5 webassign net JS Secti y 8 MacBook Air 6 8 0 5 1 0 X

Calculus

Limits & Continuitynd the domain and range of the function 6 1 g z 2 1 A D 1 00 R 0 00 C D 1 R 0 00 B D 1 0 R 0 D D 0 R 0 00

Calculus

Limits & ContinuityThe function f x x5 52x 2x 147x 98 has the graph given to the right Use the graph to factor the polynomial What is the factored form of the polynomial f x Simplify your answer Type your answer in factored form Factor completely 10 6000 12000 10 O G

Calculus

Limits & ContinuityFind the partial sum without using a graphing utility 100 50 En En n 51 n 1

Calculus

Limits & ContinuityFind the sum of the infinite geometric series if possible If not possible enter IMPOSSIBLE n 0

Calculus

Limits & ContinuitySolve the logarithmic equation for x Enter your answers as a comma separated list log x log x 48 2 X

Calculus

Limits & ContinuityDetermine whether the sequence converges or diverges If it converges find the limit If the sequence diverges enter DIVERGES 9n 20 lim an 11 an

Calculus

Limits & Continuity8 Consider the function f x 3x 5x 4 7x a Find a term that when added to f would change the end behavior of f as but not as x b Find a term that when added to f would change the end behavior of f on both sides as x and as c Find a term that when added to f would NOT change the end behavior of f

Calculus

Limits & Continuity2 It is known for a function f that as f x and as a o f x What must be true about the leading coefficient of f and the degree of f 3 Consider the graph of the polynomial function f shown a Describe the end behavior of f b Is it possible for f to have a degree of 5 Give a reason for your answer y 30 25 20 15 10 5 3 2 1 6 Go 0 10 15 20 25 30 2 3 4 5 6 X

Calculus

Limits & Continuityroblem 6 Find an integral which represents the volume of the solid obtained by rotating the region enclosed by the curves y x and y 8x about the line x 8 Problem 6 64 A 50 D G A 8 8 dy B 50 7 z 8 8 5 C a 8 2 8 2 dy 64 64 a 8 2 8 y 8 5 8 2 8 8 dv 64 Just Save Problem 6 Your Answer 8 E a 8 8 5 f r 8 8 5 8 dy F dy Submit Problem 6 for Grading Attempt 1 Attempt 2 Attempt 3 G A 4

Calculus

Limits & ContinuityProblem 6 Find an integral which represents the volume of the solid obtained by rotating the region enclosed by the curves y x and y 8x about the line x 8 64 4 7 8 5 8 2 64 D n 8 2 8 64 0 64 x 8 8 C z 8 8 2 TU 8 2 8 5 1 a 8 2 8 G 8 8 2 H 8 5 8 4 Problem 6 Select you

Calculus

Limits & Continuity10 Diyagram BD n zerinde BC kenar olan ABC genini g stermektedir B l m A ZBCA n n l s nedir B l m B Y nin de erini bulmak i in bir denklem kurun ve z n B l m C ZA ve ZB B 5y 3 4y 8 l s n belirlemek i in y de erini kullan n 146 C D

Calculus

Limits & ContinuityIn Silicon Valley a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup o the underground contamination Suppose that the required monetary pool in millions of dollars is given by the following function where x is the percentage expressed as a decimal fraction of the total contaminant removed Complete parts A through E 3x P X 1 X 0 x 1 w C Find any horizontal and vertical asymptote Find the vertical asymptote s if any Select the correct choice below and if necessary fill in the answer box to complete your choice CEILE A The vertical asymptote s is are x Simplify your answer Use a comma to separate answers as needed OB There are no vertical asymptotes Find the horizontal asymptote s if any Select the correct choice below and if necessary fill in the answer box to complete your choice OA The horizontal asymptote s is are y Simplify your answer Use a comma to separate answers as needed OB There are no horizontal asymptotes D Find the x and y intercepts Find the x intercept s Select the correct choice below and if necessary fill in the answer box to complete your choice A The x intercept s is are x Simplify your answer Use a comma to separate answers as needed B There are no x intercepts

Calculus

Limits & ContinuityUse the graph of y f x assuming f x 0 i x bord and f x 0x f to answer parts A through F Q Q AV VA A Identity intervals on which the graph of t is concave upward Choose the correct answer below OA The graph is never concave upward OB a c c e g h OC d e g h OD b c c e g h OF a b d e g h OE a b e g O G a c c d e g OH e g B Identify intervals on which the graph of f is concave downward Choose the correct answer below OA a c c e g h OC b c c e g h OE d e g h OG b ck c dk e a OB a c c d e g OD a b e g OF e g OH The araph is never concave downward

Calculus

Limits & ContinuityAssume f x is continuous on 0 00 Use the given information to sketch the graph off 1 0 3 6 7 1 2 0 f x X f x 4 22 ND 0 2 ND 0 2 Choose the correct graph below OA 3 0 0 OB 6 20 S CAFK O C Q 5 OD

Calculus

Limits & Continuitysinx1 lim 4 x 0 x 2x 6x 2x 6x How should the given limit be evaluated Select the correct choice below and if necessary fill in the answer box to complete your choice OA Use l Hopital s Rule exactly once to rewrite the limit as lim Xx 0 B Use direct substitution C lim x 0 BURD which is convenient and applicable Use l Hopital s Rule more than once to rewrite the limit in its final form as lim x 0 OD Multiply the expression by a unit fraction to obtain lim x 0 Evaluate the limit e sinx 1 eme Type an exact answer e sinx 12x 12x 12

Calculus

Limits & ContinuityProve that lim 1 X 8 lim X 8 818 In 1 a x 1 x Apply l H pital s Rule by finding the derivative of the numerator and the denominator separately 2 lim ax 1 a x lim 2 X 8 X X lim a x48 Evaluate the limit e for a 0 lim Simplify the expression before finding the limit ax 1 a x X X 1 818 a 2 a 2 A