Limits & Continuity Questions and Answers

A multiple choice test question has six possible choices a If you randomly select one of the choices what is the probability that you select the correct choice b If you randomly select one of the choices what is the probability that you select an incorrect choice c If you can eliminate two of the six choices and randomly select one of the remaining choices what is the probability that you select the correct choice d If you can eliminate two of the six choices and randomly select one of the remaining choices what is the probability that you select an incorrect choice a P correct 1 6 Type an integer or a simplified fraction 5 b P incorrect Type an integer or a simplified fraction 6 1 c P correct after elimination 4 elimination 1 Type an integer or a simplified fraction Type an integer or a simplified fraction

25 81 Select the correct choice below and if necessary fill in the answer box to complete your choice OA 25 81 Type an integer or a simplified fraction B The expression is not a real number

144 81 Select the correct choice below and if necessary fill in the answer box to complete your choice A 144 81 Simplify your answer B The expression is not a real number

O Watch the video and then answer the question given Ber Click here to watch the video Determine whether the following system has an identity element and if so what is it Choose the correct answer below O A OB O C O D

A medical researcher administers an experimental medical treatment to 200 patients The patients in the study are categorized by blood types A B AB and O The researcher observed that the treatment had a favorable outcome for 63 of the 90 patients with blood type A 13 of the 26 patients with blood type B 4 of the 4 patients with blood type AB and none of the 80 patients with blood type O Use this information to complete parts a through d a Determine the empirical probability of a favorable outcome for those patients with blood type A P favorable A 0 7 Type an integer or decimal rounded to the nearest hundredth as needed b Determine the empirical probability of a favorable outcome for those patients with blood type B Type an integer or decimal rounded to the nearest hundredth as needed P favorable B

Determine if the system has an identity If so list the identity element M D M M Q M D M D M D Q T Select the correct choice below and if necessary fill in the answer box to complete your choice OA The identity element is OB There is no identity element

Insert or to make the statement true 1 41 141 A 1 41 141

Start by drawing a number line that shows integers from 5 to 5 Then graph the real number on your number line 11 3 Graph 11 on the number line 72 Lin

In June 2010 the population of a large country was about 306 3 million people and the population of the world was about 6 420 billion people Determine the ratio of the country s population to the world s population by dividing the country s population by the world s population Write your answer as a decimal number and round to the nearest thousandth The ratio of the country s population to the world s population is Type an integer or a decimal rounded to the nearest thousandth as needed

Name all numbers that have an absol w Select the correct choice below and if necessary fill in the answer box to complete your choice O A The number s that have an absolute value of 8 is are Use a comma to separate answers as needed O B It is impossible for a number to have an absolute value of 8 1

Consider the mathematical system defined by the following table Answer parts a through 9 T X Q L T X T XI Q L T L T C L T X a Is the system closed O No Yes XO X Q CTXC Q L b Is there an identity element in the set If so what is it Select the correct choice below and if necessary fill in the answer box to complete your ch OA There is an identity element It is OB There is no identity element

Consider the following 15 4 t a Find the reference number t for the value of t 7 b Find the terminal point determined by t

D H W J PHO O No D J D H HUDHW a Is the system closed Yes J D BOHW J MHWID J J b Is there an identity element in the set If so what is it Select the correct choice below and if necessary fill in the answer box to complete your c O A There is an identity element It is OB There is no identity element

M G W P ECPMG PM G W HO WMGWP PGMPs W A The inverse element that corresponds to G is p B G has no inverse element w determine the inverse element of W Select the correct choice below and if necessary fill in the answer box to compl A The inverse element that corresponds to W is w B W has no inverse element w determine the inverse element of P Select the correct choice below and if necessary fill in the answer box to comple A The inverse element that corresponds to P is g B P has no inverse element Evaluate the following expression

Which of the following best shows that the stated case can occur The sum of two irrational numbers may be an irrational number Choose the correct answer below O A 7 6 2 6 5 6 OB 2 49 7 49 9 49 OC 7 6 2 6 9 6 OD 7 6 2 6 9 12

Perform the indicated operation without the use of a calculator and express the answer in scientific notation 30 000 2 300 The answer is 6 9x10 Use scientific notation Use the multiplication symbol in the math palette as needed

OFGE M W P une MGPM ematical system defined by the following table Answer parts a through g GPM WMGWP a Is the system closed C Yes O No W M M G W G W PGWP W P P M 300 b Is there an identity element in the set If so what is it Select the correct choice below and if necessary fill in the answer box to complete your choice A There is an identity element It is w OB There is no identity element c For each element in the set give the corresponding inverse element if it exists Start with M Select the correct choice below and if necessary fill in the answer box your choice O A The inverse element that corresponds to M is OB M has no inverse element

The following diagram is a sketch of a 16 in ruler marked using 0 5 in increments 1 2 3 5 8 9 10 11 12 13 14 15 4 6 Without using a calculator indicate between which two adjacent ruler marks the following irrational number will fall 141 in The number 141 falls between and on the ruler Simplify your answers Type integers fractions mixed numbers or decimals

Consider the following lim 3x In x X 0 a Describe the type of indeterminate form if any that is obtained by direct substitution O oo 8 8 O O O O O 0 00 1 0 858 0 88 O 0 O not indeterminate b Evaluate the limit using L H pital s Rule if necessary Use a graphing utility to graph the function and verify the result If the limit is infinite enter co co as appropriate If the limit does not otherwise exist enter DNE

Tutorial Exercise Evaluate the limit using L H pital s rule if necessary Step 1 lim X 7 The limit to be evaluated is lim X 7 49 x X 7 49 x X 7 lim X 7 By the direct substitution we have the following 49 x 0 X 7 Thus the direct substitution results in Select form

Consider the function f x 4x2 10x 8 Step 2 of 2 Find an equation for the axis of symmetry of the parabola defined by the given function Write the exact answer Do not round Answer 2 Points Keyboard

oose the correct graph for the following linear function swer 2 Points 101 5 101 S s 10 Enable Zoom Pan Ay top 5 p x 6 S A 16 Enable Zoom Pan X X 101 5 101 5 5 iol Enable Zoom Pan 5 Enable Zoom Pan x

Consider the following graph Step 1 of 2 Does the graph represent a function Answer 2 Points 10 5 HOT 10 Enable Zoom Pan

An object is thrown straight up with a velocity in ft s given by v t 32t 98 where t is in seconds from a height of 66 feet a What is the object s initial velocity b What is the object s maximum velocity c What is the object s maximum displacement d When does the maximum displacement occur e When is the object s displacement 0 f What is the object s maximum height

Perform the indicated operations and reduce the answer to lowest terr 7x 4 X 6 7x 4 x 6 7 7

inverse function f1 of the function f T T

A probability density function for the random variable X is given by p k where k is a constant What value must k be if x takes on integer values between 1 and n Hint r 0 x 1 1 r O a k O b k Ock O d k 3 1 9 2 1 oe k

Let f x x x 1 To draw the graph of f first choose some convenient values of x we have chosen x x f x x x 1 2 1 lear Help D 0 Graph of f y Do it 1 2 1 0 1 2 Then calculate f x for each value of x Check The graph of the function f consists of all possible points x f x for x in the domain of f The above table gives us a few points on the graph Use the values of f x in the table as values of y and then plot the resulting points x y 1 Adjust the points plotted below in this way 2 Then press Check to see wheher they are correctly plotted 3 To obtain the curve suggested by these points press Connect the points 2

1 Homework C355 Question 6 of 10 1 point Question Attempt 1 of Unlimited Part 1 of 3 X 14 Part 2 of 3 X Determine if the given value of x is a solution to the logarithmic equ log x 3 log3 x 26 2 1 3 Is it a solution Yes No O Is it a solution Yes No O 4 X 5 X 6 S

How many permutations are there of 20 objects when taken 6 objects at a time if a particular one of these objects must always be included a 6 201 20 6 O b 20 201 20 6 2 O c 201 20 6 2 O d 6 20 20 6 na so0 3100 6111

u x Identify the correct graph of this piecewise defined function 8 9x5 3 Enable Zoom Pan RA 100 if x 1 if x 1 4 Enable Zoom Pan A 87 200 8 4 H

A probability density function for the rando

Screenshot or sketch Points of intersection above marked and labeled Algebra Answers that are in the interval 0 to 2 stated the beshem svods not39219tra

a population of 140 000 grows 3 per year for 16 years how much will the population be after 16 years

The volume of a gas in a container varies inversely as the pressure on the gas If a gas has a volume of 410 cubic inches under a pressure of 13 pounds per square inch what will be its volume if the pressure is decreased to 8 pounds per square inch Round your answer to the nearest integer if necessary

In Exercises 19 24 write the first five terms of the geometric sequence Find the common ratio and write the nth term of the sequence as a function of n 20 a1 81 ak 1 z zak

nd a formula for the linear function depicted in the following graph 10 a 10 S Enable Zoom Pan 5 10 x

3 Answer 0 Step 2 of 2 Determine if the relation is a function If it is not identify two ordered pairs as proof Selecting an option will display any text boxes needed to complete your answer 3 Function yes o no

Consider the following relation 3x 4x 2x 2y Step 3 of 3 Determine the implied domain of the function found in the first step Express your answer in interval notation Answer

AUXISE 20 24 complete the table List the point and ordere or each vertex of the pentagon at the right 20 21 22 23 Point Ordered Pair B

The function C m 15 10 5m approximates the temperature in degrees Celsius at an altitude of m miles The function m t 0 2t approximates the altitude in miles of an airplane t minutes after taking off where t is the set of values over the interval 0 25 Find C m t Evaluate C m 25 and explain what t represents m t 0 2t

What is the element in the 2nd row 3rd column of this new 2 2 r5 4 31 2 0 3 4 4 20 B 3 3 4 ment in the 2nd row 3rd column of the new matrix is 4

When writing the solution to the partial fraction decomposition this solution Select one O a O b O C O d O e 3 X of 2 3 2 3 x x 2 2 x 2 3 x x 2 3 x2 x 2 x what is the first step of x 1 3x 2 x x 2 1 A B x 2 x 1 Ax B x 2 3x 2 x x 2 C x 1 3x 2 x x 2

Gabriel coordinates games for a youth soccer league After Gabriel has figured out which teams are playing there are still plenty of decisions to make The league plays in 2 parks and each one has 2 soccer fields Each game needs a referee and there are 3 referees on the league s roster Each game also needs one person trained in first aid and Gabriel has a list of 6 volunteers for this role How many different ways can Gabriel organize a game ways

nments Assignment 4 The number of different mammal s random variable X with CDF

19 Perform the indicated operation and reduce completely In reduced form what is the numerator x x 2 x x2 x 4x 12 x 7x 6 2x 1 O 31 4 6x 2 6x 2 3x 4 1

Consider the one parameter family of functions given by g x q a has a vertical asymptote at a O True O False lim q x 818 lim q x 8118 Determine q x 5c We classify this critical point as O a local minimum O a local maximum O neither a local minimum por a local 4e IE The function g x has exactly one critical point This critical point is at x 5c where c 0

e logistic model P t ich sentence below best describes P 0 93 2638 1 0 0303e0 1715t 100 Q A P 0 is the year no households had a personal computer B P 0 is the year all households had a personal computer C P 0 is the percentage of households without a personal computer in 1987 D P 0 is the percentage of households with a personal computer in 1987 Use a graphing utility to graph P P t Choose the correct graph below represents the percentage of households that do not own a O B Question 10 6 8 23 Part 5 of 5 seholds 100

hathematical model has been developed based on data from space shuttle launches involving the relat ky primary O rings The model stated the following formula where the number 6 indicates the 6 prima y 6 5 085 0 1156x 1 e What is the predicted number of eroded leaky primary O rings at a temperature of 80 F D rings e a whole number Round to the nearest O ring as needed What is the predicted number of eroded or leaky primary O rings at a temperature of 0 F ring s e a whole number Round to the nearest O ring as needed nd the graph of the equation y se the correct graph below Question 12 6 8 27 Part 4 of 4 6 5 085 0 1156x 1 e OR

he logistic model P n 113 3198 0 0912n 1 0 115e Question Part models the probability as a per Use a graphing utility to graph P P n Choose the correct graph below