Limits & Continuity Questions and Answers

2 The graph for f has a domain of 1 5 and range of 4 10 Let g x Find the domain and range of g x f x 3 6 4 points

f x 8 6 X SY 8 61 4 2 2 4 19 8 6 8 x

Graph each function 32 f x fool 4 2 x 3 2 6 2 2 6 y 4 00 X

e cos 0 Need Help Submit Answer 0 1 Points X 35 Read It DETAILS PREVIOUS ANSWERS SPRECALC8 6 4 030 1 3 Submissions Used MY NOTES ASK YOUR TEACHER PRACTICE ANO Find all angles 8 between 0 and 180 that satisfy the given equation Round your answer s to one decimal place Enter your answers as a comma separated list Enter your answer in degrees tan 0 21

an 3n 19 izisinin ka teriml 3 ten b y

5 309 4 glog 2 wreu keyter what is the result of the transaction

7 In the creation of a DNA profile a b C d minisatellites short tandem repeats introns exons are typically used

The graph below shows a continuous function y a t F 6 5 A 3 2 2 2 2 3 5 6 2 3 A At 3 f is increasing The function is defined as an integral f x a t dt f At a 1 f is increasing 6 For each value listed below decide if the function f is increasing decreasing or neither at that value At 4 f is increasing At a 5 f is neither At 2 f is neither 7 8 OF OF a OF OF

8 3 Does E 1 2 n 0 37 converge or diverge If it converges what is the sum

4 Determine the domain Express your answer in interval notation 5 points f x log 2 3

1 Write an equivalent statement in logarithmic form 4 points 1 100 10 000

b lim X XX x 1 X

In order to study the effects of World War II on a certain country s economy an economist used data from that country s census bureau to produce the following Lorenz curves for the distribution of income in 1935 and 1947 f x x25 Lorenz curve for 1935 16 g x x 6 Lorenz curve for 1947 Find the Gini index of income concentration for each Lorenz curve and interpret the results What is the Gini index for 1935 0 428 Round to three decimal places as needed What is the Gini index for 1947 Round to three decimal places as needed

Suppose that f is a function given as f x follows 1 x 7 We will compute the derivative of fat x 5 as First we compute and simplify the expression f 5 h f 5 h f 5 lim h 0 5 and x 5 h Then we compute and simplify the difference quotient between a f 5 h f 5 h The derivative of the function at x is the limit of the difference quotient as h approaches zero f 5 h f 5 h

PART 2 Show all your work for each opell answer without supporting work 11 15 points Consider the function f x 2x 3x 36x 4 a Find the critical point s of f x 2x 3x 36x14 6x 6x 136 Answer b Use either the first derivative test or the second derivative test the choice is yours to identify whether each critical point found in part a results in a local maximum or a local minimum for the original function f r Label each critical point as the location of a local maximum local minimum whichever is appropriate Answer c Use calculus to find the global maximum and global minimum of the function f x on the interval

2 f x x 6x 10 x Use the given zeros and the rational zeros t

function completely 3 f x x 2x 5x 6 Zero x 3 imions of which food danced in the children s heads as they slept in the poer Ju Refore Christmas

Explain what is meant when it is said that data vary How does the variability affect the results of statistical analysis Choose the correct answer below OA Saying data vary means that the values of the variable change every time they are observed Because data vary each statistical analysis of a given variable will lead to different results OB Saying data vary means that examining different types of subjects will yield different data such as examining a person and examining a car Because data vary it is impossible to compare different types of subjects such as comparing people and cars OC Saying data vary means that observations can be measured with fractions or decimals instead of only integers Because data vary it is important to make sure to accurately account for fractional observations OD Saying data vary means that the values of the variable change from individual to individual In addition certain variables can change over time for certain individuals Because data vary two different statistical analysis of the same variable can lead to different results

Evaluate the limit lim 3 tan 4x Enter a simplified multiple of or or 3n 2 X

Use 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

20 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

Graph 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

14 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

18 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

Find 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

Use 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

State 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

1 Korzystaj c 2 definicji granicy lim 2n 5 2 20 1 1 udownic

A 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

1 10 Points Compute lim sin 4x 0 2x 2x

Using 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

f x x 2x 15 xa q lim f x i X 3 find the lim

42 cos 0 1 44 tan 0

37 cos 7 2

Use 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

Find 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

Solve the logarithmic equation Round your answer to three decimal places log10 x 1 8

Find the inverse function of f informally Verify that f f x x and f f x x f x 5 x 4 f x

https 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

Use 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

All 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

Use the properties of logarithms to condense the expression Assume z 6 5 In z In z 5 2 In z 6

dp 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

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

A 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

The figure f x A d T TTTTTTTTTT

Evaluate the limit using L Hopital s rule lim 3x e t

A 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

Which 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

Write 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