Sequences & Series Questions and Answers

Use the function f x at the right Graph the translation g x f x 1 Choose the correct graph below OA Ay G B B OC Ay Ay

B b V a y X O a no solution b infinitely many solutions c one solution

12 6 5 pts each Given that cos a 13 trigonometric identities to find the exact values of a cos 0 a b tan 20 a T and cot 3 3 x 0 2 7 314 use the

Use Newton s Method to approximate the x value of the indicated point of intersection of the two graphs accurate to three decimal places Continue the process until two successive approximations differ by less than 0 001 Hint Let h x f x g x f x 2x 1 g x x 5 y f x 3 F y g x 1 2 3

Given the following table of values select the common ratio or the common difference 1 3 X x y 2 1 10 1 2 1013 1 3 9

1 point Find the interval of convergence for the given power series n x 2 n 2 n The series is convergent from x to x n 1

A store is experiencing constant growth The store recorded a total of 230 000 in sales in 2006 and 255 000 in 2011 Use a graph that displays the store s total sales as a function of time to estimate sales for 2008 and for 2012 Choose the correct graph below Let the horizontal axis represent the year and the vertical axis sales OA OB OC 300 000 200 000H 2005 2015 300 000 200 000 2005 2015 The estimated sales of the store for the year 2008 is S The estimated sales of the store for the year 2012 is S 300 000 200 000 2005 2015 Q Q O D 300 000 200 000 2005 2015 Q Q 0

The figure has a tangent line drawn at a labeled point 9500p t thousand employees 9400 9300 9200 9100 4 8 9243 1 years since 2000 6 a Estimate a second point on the tangent line t p b Calculate the rate of change of the function at the labeled point Round your answer to one decimal place thousand employees per year c Calculate the percentage rate of change of the function at the labeled point Round your answer to three d places per year

5 Graph the quadratic function f x x 8x 7 a Does the parabola open up or down b Find and plot the vertex c Find and plot the intercepts d Graph the function 10 10 8 6 8 6 4 2 4 2 2 4 6 8 NE 2 4 6 8 10

Given the following table of values you can determine the function is X 2 0 y DO 8 6 4 1 2 2 0 Linear Cubic Quadratic Exponential

5 Divide the complex numbers Give your answer in a bi form 7 3i 5 i

5 43 2 1 3 2 1 2 3 1 2 3 4 5 The function graphed above is Increasing on the interval s Decreasing on the interval s

Graph the given function by making a table of coordinates f x 2 Complete the table of coordinates 1 1 y 2 Type integers or fractions Simplify your answers Choose the correct graph below O A X 2 4 1 0 2 2 1 1 OB 1 O D 3 2 1 123 K

5 4 3 2 1 2 2 3 4 a The function graphed above is Increasing on the interval s Decreasing on the interval s 10 6 5 4 3 2 1 8 6 4 2 4 6 8 10 1 2 3 4 5 6 The function graphed above is 5 Concave up on the interval s Concave down on the interval s d

A graph of f x is shown below 10 10 5 3 2 1 2 f x 4 1 N 0 4 0 1 2 5 5 A Suppose g x f 2x 3 5 Using the graph above and the transformations applied to the function f x to graph the function g Once you have drawn your new graph save it as an image or take a picture it and upload the file as a submission

Verify the identity cos 8 sec Which sequence of steps verifies the identity O A OB O C sin 0 csc 0 sin 0 D cos 8 sec cos 0 sec cos 8 sec 0 cos 0 sec sin 0 csc 0 sec 0 sin 0 csc 0 sin 0 sin 0 csc 8 cos 0 sin 0 csc 0 sin 0 sin 0 csc 0 sec20 sin 0 csc 0 sin 0 sin 0 csc 0 cos 20 sin 0 csc 0 sin 0

For sample values X X X the sample variance is s Each x a Show that the sample variance is unchanged if a constant c is added to or subtracted from each value in the sample b Show that the sample variance becomes c times its original value if each observation in the sample is multiplied by c becomes x c n 1 x x where x n i 1 becomes CX 1 0 1 a If a constant c is added to or subtracted from each value in the sample how do the sample values x change remains unchanged n Ex is the sample mean i 1 B

How many orthogonal linear transformations T R R are there that satisfy C A and Find their matrices T 1 3 5 1 4 5

Assume that x and y can only be single digit numbers Explain whether x or y has a greater influence on this function k Le 2x 5 3 mod 3 logs 2y 50 4

Set the proper scale and plot the coordinates from the table Label x intercepts 2 1 0 1 2 11 Part 2 Graph two functions Label functions Set the correct scale f x 3x 3 and g x x 1 2 1 0 1 2 h x 11 f x g x f x g x Label the intersections of f x and g x use ordered pairs Is there a connection between Part 1 and Da 37

Consider the function f x y x 2y a 4 marks Show that lim f x y does not exist by using different path x y 0 0 toward the origin Provide a diagram to illustrate the paths that you have chosen b 8 marks Show that lim f x y does not exist by using 8 definition x y 0 0

fogx41 Drag and drop options on the right hand alce and submit For keyboard navigation SHOW MORE T 03 EDI 4 3 E 2 3 15 y g x y f x

For which values of a and b is the function f x continuous and differentiable 23 2x 5 x 2 ax b x 2

Use the horizontal and vertical line tests to determine if the graph is of a one to one function t 3 2 7 1 3 2 1 q Oone to one function Onot a function O function but not one to one

Let u 6 BLEIN and 11 3 W 3 5 Find a vector not in Span u v Enter the vector horizontally as x1 22 23 3 6 2

Which of the following are subspaces of R U x 2y x y 3x y x y R 4 V x y x y x y R See bel W x y z 3x y 0 is a plane X x z z x z R span 1

2 3 215 24 Drag and drop options on the righahand side and submit Fer keyboard negation go 4 ir Am MODE Not defined y g x

The following figure shows that 5 by 5 square tiles can be used to cover a floor that measures 30 by 70 Each square in the figure represents a 5 by 5 square tile a List all of the sizes of square tiles that can be used to tile the floor What is the largest size of square tile that can be used b How many square tiles of the largest size are used to cover the floor inch es long a The possible square tiles have sides that are Type whole numbers Use a comma to separate answers as needed HEE inch es long The largest square tile that can cover this floor has sides that are Type a whole number b The number of tiles of the largest size required to cover the floor is 4 30

Find the length x to the nearest whole number X 26 350 550 Ext T X

A graph of a function f is given below 2 y 15 r 10 5 Find 1 and f 7 4 2 6 K17 2 GF 8 100 X

For the following exercise find f a for the function 40 x x 1 x 14937 201 XABARD Preview

Use the values listed in the table below to evaluate or solve C 3 f x 9 Find f 3 f 3 2 8 S 1 4 0 3 1 9 2 3 2 3 4 7

Express log b log b 25 Pq 4 7 25 pq in terms of sums and differences of logarithms 4 7 mb m b Simplify your answer

For n 1 and x 0 1 let n fn x j 1 cos jx 2 j j 1 Does the sequence fn converge Does it converge uniformly on 0 1 Pr your assertion

Answer the following questions about the equation below 6x3 25x2 24x 5 0 a List all rational roots that are possible according to the Rational Zero Theorem Choose the correct answer bel OA 1 12 13 16 OB 1 12 13 6 5 OC 1 15 1 5 D 1 5 t 1 2 H 95 H H 0 6 H 6 5 1 5 1 5 H

A flexible cable hanging between two poles is modeled by H z 20 25 cosh bers the height is in heat Find the slopes of the cable at the point where X 10 Show all yours rounded to 3 decimal places

Question 5 10 8 6 4 2 10 Equation 5 5 10 2 4 6 8 10 Q Write the equation of the line shown Be sure to use the correct variable

The graph of a rational function fis shown below Assume that all asymptotes and intercepts are shown and that the graph has no holes Use the graph to complete the following a Write the equations for all vertical and horizontal asymptotes Enter the equations using the and button as necessary Select None as necessary Vertical asymptote s 0 Horizontal asymptote s 0 Chark all that apply 08 0 0 0 0 0 0 0 0 0 0 a Write the equations for all vertical and horizontal asymptotes Enter the equations using the and button as necessary Select None as necessary Vertical asymptote s Horizontal asymptote s b Find all x intercepts and y intercepts Check all that apply x intercept s 0 1 0 3 0 6 None y intercept s 0 6 0 2 0 3 None c Find the domain and range of f Write each answer as an interval or union of intervals Domain MORE BUD 8 08 None 0 0 0 0 x OUD

Express in terms of sums and differences of logarithms log a b 7 log a b

The measure of an angle is standard position is given Find the exact values of cos 0 and sin 8 Choose all that apply 2 radians Select one or more cosine is 0 a b c cosine is 1 cosine is 1 2 sine is 1 Od O e Of sine is 0 sine is 1 2

Find the LCD of the following Do not combine fractions 6 5 5x 35 6x 42 The LCD is Simplify your answer

A B O D 2 A1 4 3 2 8 1 4 2 3 C 4 1 2 3 D4 1 3 2

Use the circle to find the length of the indicated arc Round your answer to the nearest tenth The arc is Check 1 jm 3 cm t cm Use the circle to find the length of the indicated arc Round your answer to the nearest tenth

find the domain of f of g x where f x 1 x 4 and g x square root of x 5 interval notation

For a certain exponential function whenever a changes by 1 unit the value of y changes by 10 Using this information complete the following table I 0 1 2 5 5 6 5 y f x 9 5 0417 4

The graph shows the depth of water at the end of a boat dock y Depth feet 10 0 0 3 6 9 12 15 18 21 24 Hours after Midnight a Find the amplitude of the graph b Find the period of the function OU a The amplitud

measure of the angle in standard position is O d

Consider the integral 5 Hint Recall the formula k k 1 Let n be a positive integer Let P be the partition of the interval 0 5 with n equal subintervals Find and simplify the upper Darboux sum U f P where f x 4x 3 Then take the limit of the sum as n to find the integral itself 4x 3 da n n 1 2

Which of the following graphs is not a function Select one Oa O b 3 2 SH 14 0 1

2 3 6 Let A 0 6 0 Given that A 0 0 A and A 1 1 4 0 1 the eigenvalue 6 1 mark 0 None of the options Which of the following vectors are eigenvectors of A associated to