Questions

Suppose f g are continuous functions where f 9 19 and lim 6f x 2g x 122 x 9 Then g 9 Question

Consider the graph shown Check all that apply lim f x exists x 2 a f 2 exists None of the above

The region bounded by the graphs of x 0 x Iny and x 7 6 Iny in the first quadrant is revolved about the y axis What is the volume of the resulting soll The volume is Type an exact answer

2x 6 if x 4 Let f x 34 5x if x 4 if x 4 12 eta Determine whether f x is continuous at 4 If f x is not continuous identify why Not continuous f 4 is undefined Not continuous lim f x does not exist x 4 Not continuous lim f x f 4 x 4 The function is continuous at x 4

The graph of y f x has the following features lim f x 3 f x 2 f x f x xxx lim TH lim 24 1 lim 1 12 Which of the following might be a graph of y f z 8 78 8543 2 3 2 1 4 3 2 20 Z d a 9 9 4 3 2 3 16 112 84 4 5 6 3 2 8 7 6 4 2 F 2 12 4 4 9 b 8

Let R be the region bounded by the following curves Let S be the solid generated when R is revolved about the given axis If possible find the volume of S by both the disk washer and shell methods Check that your results agree y O A 1 x 1 B X y 1 revolved about the x axis Set up the integral s that gives the volume of the solid as a single integral if possible using the disk washer method Use increasing limits of integration Select the correct choice below and fill in any answer boxes within your choice dx Type exact answers JOdx dx Type exact answers

Suppose f x has the following values I 1 9 1 99 1 999 2 1 9 5 99 5 999 C 2 001 2 01 2 1 9 005 9 05 9 5 What value of c would make f x continuous at x 2 Enter a value of c If no value exists enter DNE

Use synthetic division to show that x is a solution of the equation and use the result to factor the polynomial completely List all real solutions of the equation Enter your answers as a comma separated list x x 14x6 0 x 2 6 X

suppose Iim f x x 2 The graph of y f x might look like select all that apply

Suppose f x is defined at 1 and lim f x exists but lim 4 1 1 The graph of y f z might look like select all that apply None of these f x f 1

Consider the graph shown Check all that apply a f 2 exists lim f x exists 112 None of the above

Suppose f x IS The graph of y f x might look like select all that apply Q de x 1 CO

Let f x 4x 3 if x 1 12 5x if x 1 Determine whether f x is continuous at x 1 If f x is not continuous identify why Not continuous lim x 1 f x f 1 Not continuous f 1 is undefined Not continuous lim f x does not exist x 1 The function is continuous at x 1

x 1 not exist The graph of y f x might look like select all that apply Q

Consider the graph shown Check all that apply f 1 exists lim f x exists x 1 None of the above

The graph below is the function f x 54 3 2 lim x 1 54327 lim x 1 2 he 72 S Find the following If no value exists enter DNE f x f x 12 lim f x x 1

The graph of y f z has the following features e e f 2 1 lim f x 2 2 lim f x 2 2 2 Which of the following might be a graph of y y f x

The region is formed by the graphs of y 3 2x and y 8 x Find the volume of the solid obtained by revolving the region about the x axis ronion about the x axis is CLE

Starting at the same point on a straight road Anna and Benny begin biking with velocities in mi hr given by VA t 2t 2 and VB t 5 t respectively Complete parts a through c below 10 0 01 2 3 4 0 1 2 3 4 L hour s 4 hour s while Anna rides 8 miles in hour s while Benny rides 8 miles in V 0 0 1 2 3 4 5 What does this mean geometrically A The area under the line representing Benny s velocity from 0 to 1 is more than the area under the line representing Anna s velocity from 0 to 1 OB The line representing Benny s velocity is decreasing while the line representing Anna s velocity is increasing OC The lines intersect at a t value before the given time indicating that Benny has passed Anna OD The area under each line from 0 to 1 is the same for both riders 4 b If the bikers ride for 1 hour who rides farther Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals A Since Benny rides 4 5 mile s and Anna rides 3 mile s Benny rides farther OB Anna and Benny both ride mile s OC Since Benny rides mile s and Anna rides mile s Anna rides farther hour s hour s 07 13 012 34 c If the bikers ride for 8 miles who wins the race Interpret your conclusion geometrically using the graph in part a Select the correct choice and fill in the answer box es to complete your choice Type integers or decimals OA They tie in the race because they both ride 8 miles in O B Benny wins the race because she rides 8 miles in OC Anna wins the race because she rides 8 miles in Save

A large tank of fish from a hatchery is being delivered to a lake The hatchery claims that the mean length of fish in the tank is 16 inches and the standard deviation is 4 inches A random sample of 36 fish is taken from the tank Let X be the mean sample lengt of these fish What is the probability that x is within 0 5 inch of the claimed population mean Round your answer to four decimal places USE SALT

Problem 2 7 P Figure 2 shows the phylogenetic relationship between a potentially recombinant variant CRF 7 of HIV 1 and the representatives of subtypes B and C These phylogenies were reconstructed from the coding sequences of four HIV genes gag pol env and nef gag B CRF 7 pol C B CRF 7 env B nef B CRF 7 CRF 7 C Figure 2 Phylogenetic relationships between the variant CRF 7 and subtypes B and C of HIV 1 reconstructed from four genes 1 3 P If CRF 7 is indeed a recombinant where on the HIV chromosome i e between which genes are the recombination breakpoints The order of genes in Figure 2 corresponds to their order in the HIV genome 2 4 P If CRF 7 is indeed a recombinant indicate which subtypes likely donated which genes to CRF 7

he region is formed by the graphs of y 3 x and y 4 x Find the volume of the solid obtained by revolving the region about the x axis The volume of the solid obtained by revolving the region about the x axis is PREURE

Problem 1 10 P Figure 1 shows a phylogenetic tree of a small outbreak of bacterial pathogen Colors represent patients from which the samples were drawn Patient 1 Patient 4 Patient 2 Patient 5 Patient 3 Figure 1 Phylogenetic tree of the outbreak 1 1 5 P For each patient identify the MRCA of all their isolates Circle and label it on the tree 2 5 P Infer the transmission chain that most parsimoniously explains this phylogeny

Required information Let P x be the statement the word x contains the letter a What is the truth value of P true The truth value is Click to select Click to select false true

Suppose the following plate is placed on a vertical wall so that the top of the plate is 1 m below the surface of a pool that is filled with water Compute the force on the plate 3 A plate shaped like an isosceles triangle with a height of 3 m and a base of length 2 If a y axis in the vertical direction is drawn on the face of the triangle where the origin is the vertex of the triangle find the width function w y for each value of y on the face of the triangle w y m The force on the plate is N Tupe an integer or decimal rounded to one decimal place as needed eufee

Required information Let Q x y denote the statement x is the capital of y Determine the truth value of Q Detroit Michigan The truth value of Q Detroit Michigan is Click to select Click to select true false

Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to th Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p A p q q p p q og p p q T q Click to select T P q T Click to select FT Click to select K The given conditional Click to select Click to select True False F Click to select Click to select Click to select Click to select statement is not a tautology 4

Required information Let P x be the statement the word x contains the letter a What is the truth value of P orange The truth value of Plorange is Click to select Click to select false true

The region is formed by the graphs of y 3 2x and y 8 x Find the volume of the solid obtained by revolving the region about the x axis The volume of the solid obtained by revolving the region about the x axis is E

Find the length of the following curve 2 y In x x 1 for 10 145 The length of the curve is Type an integer or decimal rounded to three decimal places as needed

Find the mass of the thin bar with the given density function p x x 8 x for 0 x 2 The mass of the thin bar is Gyne an exant porwer units

Write and simplify the integral that gives the arc length of the following curve on the given interval Then use technology to approximate the integra x 2 4 on 3 9 The integral that gives the arc length of the curve is L JOdx

The Customer Service Center in a large New York department store has determined that the amount of time spent with a custome about a complaint is normally distributed with a mean of 8 3 minutes and a standard deviation of 2 3 minutes What is the probability that for a randomly chosen customer with a complaint the amount of time spent resolving the complaint will be as follows Round your answers to four decimal places USE SALT a less than 10 minutes 0 7700 b longer than 5 minutes c between 8 and 15 minutes 0 5501

etermine the area of the region shown to the right y x 3 y 6 x 3

Determine the area of the given region The region bounded by y sin X 2 and y cos The area of the given region is Type an exact answer using radicalo X 2 on 3t 5t 2 2

Complete the truth table given below for the conditional statement p a A q p pa q P Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables pq r TIT T TIT F TFT FIF T T F T Click to select F T T F p q T T F F T T T T F T F T The given conditional statement is a tautology Click to select Click to select Tru FIT FF 9 r T Click to select v pg 91 T Click to select F F T F Click to select p r T F T Click to select T T T T T Click to select

Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this part Show that each of these conditional statements is a tautology by using truth tables Complete the truth table given below for the conditional statement p V q A pr q n r r p V q p1 9 1 T T F T F F T F T F T F P T T T T F F F F q T T F F T T F F p V q T T T T T T Click to select Click to select The given conditional statement is a tautology Click to select Click to select True False p 1 T Click to select Click to select F T T T T Click to select F Click to select T F F Click to select T T F T T p V q p 9 T F Click to select F Click to select F F F pVg p 1 q r T Click to select T Click to select T Click to select T

pA pv q q A p q v q pv T by negation law p pv q q pv qv q by associative law FV p q q by negation law pvF by negation law pv q vq by De Morgan s law

Required information NOTE This is a multi part question Once an answer is submitted you will be una Fill the given truth table Fill the truth table for Click to select p You must provide an Click to select noving to the next part PAP Click to select P p

If a fluid has a low viscosity and suddenly releases a small amount of gas let s say CO2 will it explode Hint think of opening a can of soda pop OYes it will explode No it will not explode

Recall What is the difference between magma and lava Magma is melted rock underground and lava is melted rock at the surface Magma is melted rock at the surface and lava is melted rock underground I m confused Aren t they the same thing

Find the area of the shaded region shown in the figure which is not shown to scale

Complete the truth table given below to verify the first De Morgan law p Aq p V q p q 7P79 TT Click to select F p q Click to select T PV q FF Click to select T TA FIT FT Click to select F Click to select TF Click to select TIT T T V

Assume that IQ scores are normally distributed with a standard deviation of 15 points and a mean of 100 points If 120 people are chosen at random what is the probability that the sample mean of IQ scores will not differ from the population mean by more than 2 points Round your answer to four decimal places LAUSE SALT

Iris lens optic disc fovea iris cornea sclera cornea retina lens Question 10 What is the visual pigment used to capture light in most animals Rhodopsin Melanin Transducin 1 pts

Required information NOTE This is a multi part question Once an answer is submitted you will be unabl Fill the provided truth tables and check whether the given conditional statements a contingency pv q Click to select Click to select T Click to select F Click to select The given conditional statement is Click to select Click to select tautology P T T F F 9 T F contingency contradiction p pv q Click to select Click to select Click to select Click to select V

P T T p p q Click to select Click to select Click to select Click to select Click to select Click to select Click to select The conditional statement is p p q is a Click to select Click to select F Required information NOTE This is a multi part question Once an answer is submitted you will be L Fill the provided truth tables and check whether the given conditional stateme contingency F q T F T p F F T T F p q Click to select contigency tautology contradiction

P T TFF Required information NOTE This is a multi part question Once an answer is submitted you will be Fill the provided truth tables and check whether the given conditional staten contingency q paq F T Click to select Click to select Click to select F Click to select T p q p Click to select Click to select Click to select Click to select The conditional statement p A q pis a Click to select Click to select contradiction contigency

Dopamine Serotonin Acetylcholine Melatonin Question 6 The organ of Corti is associated with which special sense Taste Hearing

Fill the following truth table P 9 T T T F T F Required information NOTE This is a multi part question Once an answer is submitted you will be unable to return to this pa Show that each of these conditional statements is a tautology by using truth tables F F P F F T T pv q Click to select T T F p pv q F Click to select T Click to select PA pv q T T Click to select q