Sequences & Series Questions and Answers

em 4 The graph of f is given to the right Which of the below graphs is a graph of its antiderivative f

6 State whether the product of 3 and 9 is rational or irrational Explain your answer

1 2 3 4 X Need Help Read It Additional Materials 1 6 9 12 Submit Answer Tech Guide Excel Tech Guide TI 83 84 Tech Guide TI Nspire

A woman who has recovered from a serious illness begins a diet regimen designed to get her back to a healthy weight She currently weighs 105 pounds She hopes each week to multiply her weight by 1 08 each week a Find a formula for an exponential function that gives the woman s weight w in pounds after t weeks on the regimen

8 Huy borrowed 4500 from a bank at a rate of 5 per year compound interest He paid back the money and interest at the end of 2 years How much interest did he pay

Write a polar equation for an ellipse which a has a focus at the pole vertex at 28 0 and e 7 ep Write a polar equation using the standard form r 1 e cos 0 r Simplify your answer

4 Show that the sequences of functions f n k 1 1 x converges k 0 R defined by f x n pointwise to f x uniform 1 1 x 1 but the convergence is not

Write the complex number in polar form with argument 0 between 0 and 2 5

3 x 3x 2 0 5 0

201 12 A C 201 nm 8m 15 1 M B D A 12 12 271 27 A 4x 2 C 8x B DI an

Lesson Quiz A 1 Factor each of the following polynomials 5 points 9n 49 c 729

7 7 A C m 2mn 1 32mm B 8n13 D m n 8 A m 2pm 2m n B 8m n D 32m n 12

21 6 1 7 3i 22 9 51 11 21

Determine the intervals of the domain over which function is continuous Select the correct choice below and if necessary fill in the answer box to complete your choice OA The function is continuous on Type your answer in interval notation B The function is not continuous 4 3 2 Ay 5 4 3 2 1 CO NO 5 2 3 4 5 6 X

oblem 1 Consider a quantum mechanical system with three states At each step a particular particle transitions from one state to a different state Empirical data show that if the particle is in State 1 then it is 3 times more likely to go to State 2 at the next step than to State 3 If it is in State 2 then it is 8 times more likely to go to State 3 at the next step than to State 1 If it is in State 3 then it is equally likely to go to State 1 or State 2 at the next step Let A be transition matrix for this markov chain Find a31 932 and a33 i e find the last row in the transition matrix

Exercise 2 10 points Let T VV be an invertible operator and let A be eigenvalue of T 1 4 points Prove that A 0 2 6 points Prove that is an eigenvalue of T

3 Simplify Your answer should contain only positive exponents 11 a 12 12 4k A 16a8 A K 2 C 1 13 A 3 C 15 21 4v A 4v 1 C 2v 17 1 256a4 ww A C 4m 4nm 1 n 2m 1 6 4 3m n B D B 1 D 3 1 a B 4 D 2v B D m n 4 m 14 16 18 14 4 A 4 4 C 4 16 2x 3 A 4x C x 18 A C 2u v 2u v 1 vou 1 2v B 64k D 16k6 B D B B D 13 14 3 x 2 1 2u

Let V R Redefine addition and scalar multiplication in the following wa 0 0 0 0 0 by Is V a vector space under this new addition and scalar multiplication A Yes B No b a

Simplify 125xy A 6y x 2x B 2x 7y C 5y 5xy

3 135k7 A 3k 5k B 4k 6 C 2k 3k D 2k 4k

Identify the expression which is not equivalent to the others A p B p C VP D 1 p3

Simplify 72 A 4 B 7 2 4 3 C

A B 2T 5 C 3x D V

2 3n A 3n B 2n C 3n D D 9n

Sketch and find the coordinates of the point corresponding to each angle on the unit circle P is at 90 P Q is at 90 Q i R is at 360 And i

11 13 Simplify Your answer should contain only positive exponents 11 a 12 12 4k A 16a A k 2 C 1 1 256a C 13 w w w w 3 3 A 36 26 B D D B 1 1113 1 1 14 4 3 4 A 4 C 4 14 B 64k D 16k B D IT ZO

K Use an identity to write the expression as a single trigonometric function 1 1 cos 142 2 cos 142 2 0 Type an exact answer

K A 1 1 and 0 x 2 determine the exact value of cos 2 Given that cos cos Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

Use a half angle identity to find the exact value cos 165 Which half angle formula should be used to find the exact value of cos 165 Select the correct choice below and fill in the answer boxes to complete your choice Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OA cos 165 cos OB cos 165 cos OC cos 165 cos 5 2 OD cos 165 cos H 2 2 t 2 1 cos 2 1 cos 2 1 cos 1 cos 1 cos 1 cos

Simplify the expression by using an appropriate identity Do not use a calculator cos57 cos33 sin57 sin33 COL Write the expression using the sum or difference formula for sine or cosine Choose the correct answer below OA cos57 cos33 sin57 sin33 cos 57 33 cos 24 B cos57 cos33 sin57 sin33 cos 57 33 cos 90 OC cos57 cos33 sin57 sin33 s sin 57 33 sin 90 OD cos57 cos33 sin57 sin33 sin 57 33 sin 90 Points 0 5 of The exact value of cos57 cos33 sin57 sin33 is Simplify your answer including any radicals Use integers or fractions for any numbers in the expression Rationalize all denominators

K Given that sin 0 sin 20 cos 20 2184 7225 13 and cos 0 0 determine the values of the sine and cosine functions for 20 85 Type an integer or a simplified fraction Type an integer or a simplified fraction

Write the expression as a function of x with no angle measure involved sin sin ALG T 4 cosx sinx C X 2 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression

Given that sin 8 sin 20 Question 1 5 5 7 Part 1 of 2 Type an integer or a simplified fraction 7 and cos 8 0 determine the values of the sine and cosine functions for 20 25

Save The formula S 16t is used to approximate the distance S in feet that an object falls freely from rest in t seconds The height of a building is 1317 feet How long would take for an object to fall from the top The object would fall for seconds Simplify your answer Type an integer or a decimal rounded to the nearest tenth

Suppose A B and C are positive constants and x y C Show that the minimum value of Ax By occurs when BC and y AC A B A B N

6 6 points What is the end behavior of p x You may describe it with words symbols or a sketch

Use the polynomial p x 3600x 0 4x 500x 24x to answer questions 5 and 6 5 6 points Find the degree of p x and leading coefficient of p x

2 2 sin 2 z 7 b Consider the function y 2 sin What is the amplitude What is the period What is the horizontal shift Sketch a graph of the function on the axes below

APPLICATIONS Functions and YOSI Your monthly cell phone plan is 49 99 It includes 500 anytime minutes and charges 0 45 per minute for additional minutes The following function is used to compute your monthly cost in terms of minutes used can 49 99 if 0 x 500 L 45x 175 01 if x 500 Compute the cost of your cell phone for the following months Minutes Cost January 400 C x February 525 March rapns 600

Use the following functions to perform the indicated operation f x 3x 9 22 m h x g x x 12 24 fog x and sate whether f and g are inverses c x x 3 h x x 5 23 2 x Restriction 25 m c 2 m x x 2x 7

7 Santiago s weekly income after working h hours can be described by the function f below 13 5h 0 h 40 20 25h 270 h 40 Which of the following conclusions is correct f h A Santiago gets paid 13 50 an hour for up to 40 hours and an additional 20 25 per hour for hours beyond 40 B Santiago has to pay 270 in taxes if he works more than 40 hours in a week C Santiago gets paid 1 5 times his hourly rate for hours he works beyond 40 hours D If Santiago works 43 hours he gets paid 870 75

3 3 2x 5y 10 4 4 5x 3y 9 T ZOO

A3 4 3 3 2x 5ps 10 M 5 6 4 5x 3p 9 7

5 Algebra Prep 1032 Kuli Software lur SUM 2 Q2 Solve each system by elimination 5 6y 42 18x 4x 8 3y A 4 1 B 4 1 reserved 6 6 3y 3x 15 9 3x 2y A 7 5 B 7 8 ZOO

9 10 10 ys y2 x 7 zoom in

12 When police officers investigate a car crash they can estimate the speed the car was travelling by measuring the skid distance Skid Distance of a Car Skid distance m 160 120 d 80 40 0 S 40 80 120 Speed km h a Why are the points on the graph connected b Estimate the domain and range of the graph Are there any restrictions on the domain an range Explain

Find functions f and g so that fog H x 9x 1 5 Choose the correct pair of functions OA 5 f x x g x 9x 1 C 5 f x 9x 1 g x x O B f x x g x 1 9 O D x 1 f x g x x 9

2 If f x x 3 and g x then which of the following does fog x equal X Choose the correct answer below O O O 2 x 3 2 X N 2 3 3 2

3 4B Exit Ticket Divide the following polynomials using any method of your choosing 77x 5x 57x 71 x 10 x x 10

Points A B C D and E are collinear and in that order Find AC if AE 50 and CE x 32 AC