Sequences & Series Questions and Answers

n 1 7 Find the Maclaurin series for cos x x sin x What is the radius of convergence 8 Use Maclaurin series to find

Which graph below represents the map shown at the right i e doorways become edges A D D C C B B E E OUTSIDE CASE E ROOM A ROOM D ROOM C T ROOM R 11 ROOM E

Question 4 25 points The table at the right shows the times and tasks that must be completed to create a school s yearbook Which EST graph below correctly represents the information in the table Task Start A Create a guest list B Create a list of snack foods party favors and decorations C Purchase Make Invitations snacks decorations party favors D Mail invitations at the post office E Wait for response to the RSVP on the invitation F Clean the apartment G Decorate for the party H Cook and set out snacks I Get Dressed and Ready J Host the Party K Clean Up Finish Time hours 0 0 5 0 3 2 5 1 0 36 0 3 5 1 2 1 5 1 0 3 5 2 5 Prerequisites None None A B C D E F E G H I J

number of colors needed to color the graph 2 F B E

This is the graph of function f Function g is defined as g x f x What is the graph of g

Hamilton Circuits Paths Which of the below is the only one that CANNOT be created with the graph shown Euler Path Euler Circuit Hamilton Path Hamilton Circult H G R

Write a set of parametric equations for the ellipse which begins at the point 1 2 at time t 0 then passes through 2 1 at time t 5 2 at time t Note The answers should be functions of t x t y t 2 5 at time t before returning to 1 2 at time t RA

Distance from the Station miles Commuter Train Distance 30 25 25 20 15 10 S 0 Formula Sheet 10 20 30 40 50 60 70 80 Time minutes Calculator Referer Type your answer in the box You may use numbers a decimal por and or a negative sign in your answer Based on the graph what was the average speed in miles per minute of the train during the interval of 30 to 40 minutes

Exhibit two different bases for the column space of the matrix A where 201 2 0 1 1 A 1 0 3

Choose the graph of y log 5 O O O K 77 166 s 30

Write as the sum and or difference of logarithms Express powers as factors Joxe 2 logs

Find the inverse of the following one to one function 2 3 1 9 0 2 1 8 The inverse of the function is Type an ordered pair Use a comma to separate answers as needed

Write as a single logarithm Express coefficients as powers inside the logarithm 8 ln x 4 ln y 9 ln z x8y4 x9 X

The function f x has a zero of 3 with multiplicity 2 Which is true based on the given information O Since 3 is an odd number the graph touches but does not cross the x axis at 3 O Since 3 is an odd number the graph crosses the x axis at 3 O Since 2 is an even number the graph touches but does not cross the x axis at 3 Since 2 is an even number the graph crosses the x axis at 3

How many weeks would it take to increase the debt of a simple discount loan by 175 if the annual simple discount rate is 27 Round your answer to the nearest week

Bill took out a 5 year loan to buy a car If the loan carried an annual interest rate of 4 2 and he made monthly payments of 420 how much interest did he pay Round your answer to the nearest dollar

Arnold dropped a ball during the bouncing ball activity and recorded its height in a table Part of his table is shown below Bounce Height Number cm 0 1 2 3 y 4 a 84 5 67 6 What was the rebound ratio of his ball C 54 1 b At what height did he drop the ball rounded to the nearest whole number Write an equation that represents his data

Below is the graph of f x x3 4x 5x 9 4 12 10 Identify the following Real zeros 2 Relative local minima Relative local maxima Extreme absolute minimum Extreme absolute maximum Interval s of increase Interval s of decrease XA

Find the probability of exactly 6 successes in 7 trials of a binomial experiment in which the probability of success is 80 P Round to the nearest tenth of a percent

Find the probability of no failures in five trials of a binomial experiment in which the probability of success is 30 P Round to the nearest tenth of a percent Enter

Below is the graph of f x x4 2x 3x 4x 4 2 Identify the following Real zeros 61 Relative local minima Relative local maxima Extreme absolute minimum Extreme absolute maximum Interval s of increase Interval s of decrease 2

W Shown below is the graph of a function Assume all critical points are within the viewing window Which statement s could be true 5432 10 8 6 10 30 XA EDEAR VES The function has a zero of 2 with multiplicity 2 The function has a zero of 0 with multiplicity 2 The leading coefficient is negative The function could be a 4th degree

Condensing Logarithms 11 4 log 3 log x 12 log 6 2log x 2 log y log 6 13 log 4 4log 2x Name 14 4log x 2 log x log 3 log 2 15 2 log x log 3 log y log x 16 4 log x log y log 2 ins

The graph of a polynomial p x is shown below Select the answer if it represents a characteristic of p x Y 40 32 24 16 of 2 1 Oh 16 24 32 40 It could be a 3rd degree polynomial The zero x 0 could have multiplicity 2 The zero x 2 could have multiplicity 2 p x has a negative leading coefficient 0

6 2 log H log 6 log x log 3 1og2 log x 3 log 1022 4 log 5x y 5x 5 Ioal 7 log 8 log 6x 9 log Say 10 log 5

olve 9 x 6 1 17 all real numbers are solutions there is no solution click on I

Alexander is a teacher and takes home 96 papers to grade over the weekend He can grade at a rate of 11 papers per hour Write a recursive sequence to represent how many papers Alexander has remaining to grade after working for n hours

Evaluate the following sum 41 k 3 41 k 3 1 k k 1 1 k k 1 11 Hint 1 k k 1 1 k 1 k 1

State the domain and range of logg z Domain Range Select the graph of logg z O O 3 hap 3 9 5 5 4 3 N 1 4 3 123 4 5 67 8 9 10 q 6 7 8 9 10 O O A 4 5 5 Ha 3 Sy 7 7 3 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 La 8 9 10

You have one type of chocolate that sells for 4 60 lb and another type of chocolate that sells for 7 20 lb You would like to have 10 4 lbs of a chocolate mixture that sells for 5 70 lb How much of each chocolate will you need to obtain the desired mixture You will need and lbs of the cheaper chocolate lbs of the expensive chocolate

You need a 15 alcohol solution On hand you have a 315 mL of a 5 alcohol mixture You also have 60 alcohol mixture How much of the 60 mixture will you need to add to obtain the desired solution You will need

14 n 11n 10 4n 36 2 n 9

15 Need Help 65 1 10 into Simplify Simplify Simplify Simplify Simplify

f in 5 3 4 5 5 3 8 3 8 3 11 3 8 3 11 3 9 29 5 h 5 3 5 3 3 2g 1 1 100 2g 2g g 29 L 10 7 2 2 c 8 7 8 6 10 5 8 5 Select Simplify Select Simplify Select Simplify Select Simplify Select Simplify Select C

Multiplicative Identity Property 14 1 14 1 14 e 14 1 14 1 0 4 1 4 1 14 41 14 0 1 1 14 d Associative Property of Multiplication 0 9 0 4 3 0 3 3 G 3 H Multiplicative Inverse Property 13 13 3 13

Determine whether each of the following is an expression or an equation a 3x 6 O expression O equation b 4x 8 expression equation c 2 y 7 expression equation d 5 y expression

Use the given property of rational numbers to complete each equation a Additive Inverse Property 7 7 1 2 1 22 7 7 0 1212 1 0 171 2 1 2 2 21 12 20 0 1 2 1 2 2 21 2 20 7 1 2 0 171 2 S 7 12 1 0 b Distributive Property of Multiplication Over Subtraction 1 0 3 1 4 8 9 4 3 0 1 2 1 4 8 4 1 1 1 1 10 10 1 3 0 1 1 1 1 8 4 9 4 3 1 48 8 3 3 2 1 4 8

function to complete the following statement As x 2 f x As x 2 f x 10 8 10 8 6 4 2 4 b 4 6 8 10 D X 6 8 10 Qu Asymptotes are shown as dashed lines The horizontal asymptote is y 3 The vertical asymptote x 4 and x 2

swer 2 Points f x 2x 7 answer rounded to the nearest hundredth Keypa Keyboard Shortc

The function f is given by the graph below 10 Answer 5 10 101 5 y Enable Zoom Pan 5 10 Step 1 of 2 Use the graph to determine the locations and type of the local extrema Write DNE for all extrema that do not exist Separa answers with a comma if necessary

Find the probability of exactly three successes in eight trials of a binomial experiment in which the probability of success is 45 P 3 56 0 45 0 55 8 3 Solve part of the answer 0 45 Round to 4 decimal places

Assume that the domain of the sequence is all natural numbers Find the general term of the arithmetic sequence then find the indicated term of the sequence The correct formula to represent the general term of the arithmetic sequence is an 0 Simplify your answer Type an expression using n as the variable a10 Simplify your answer an A 20 18 16 14 12 10 8 6 4 2 2 4

Write a formula for the general term the nth term of the arithmetic sequence Then use the formula for an to find a10 the 10th term of the seque 7 3 1 5 an Simplify your answer

b f x g x 1 3x 7 1 3x x 0 0 f g x 1 8 f x Of and g are inverses of each other fand g are not inverses of each other

00 x no f x 5x2n 4 1 5 2 c 0 Determine the interval of convergence Enter your answer using interval notati

Part 2 Graphing Exponential Functions Directions Graph each exponential function by creating a table then identify its key 10 11 1 3 y 2 X Xx 0 Y 1 12 Y

12 11 10 9 SO D O 19 7 t 24 D 8 9 10 11 12 Give the equation for the function whose graph appears above Use f x as t

Jse Newton s method to estimate the two zeros of the following function Start with x 0 for the left hand zero and x 5 for the right hand zero Then for each case find X2 3x x 9 X0 0 then x

For the following triangle solve for B Enter your answers as a comma separated list If there is no solution enter NO SOLUTION Round your answers to the nearest degree A 120 b 20 cm a 60 cm one solution Use the results to explain why the triangle has the given number of solutions O Since sin B 1 only one triangle is possible O Since 180 B 90 and there can only be one obtuse angle in a triangle only one triangle is possible Since sin B 1 only one triangle is possible and there can only be one acute angle in a triangle only one triangle is possible Die 1000

The weekend weather forecast is calling for a high temperature of no more than 87 degrees Fahrenheit Use the following graph to write an inequality that models the situation Saturday s Forecast F 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 O a t 87 b t 87 O c t 87 O d t 87