Sequences & Series Questions and Answers

The point P y lies on the unit circle shown below What is the value of y in simplest form P x y Note the figure is not drawn to scale 1 0

Evaluate the function for the indicated value Evaluate f 3 7 x 1 f x x 11 1 x 3 5 x 3 Select one O a 7 O b 5 O c 3 O d 4

3 For the function defined by f x x x 1 2x 1 x 1 Part 1 Evaluate f 0 A Identify the function that will be used when x 0 1 poin B Find the value of this function when x 0 1 point

Find the value of the expression See Examples 3 5 Objective 2 3 75 3411 4 3 2 32 5

POSSIBLE POINTS e has one side that is 5 units long one 25 angle and one 90 angle Complete the two diagrams to create two different triangles with these ements Label the 90 angle in each diagram UND Redo Triangle 1 25 Triangle 2 25 D

For the function whose graph is given state the following If the limit is infinite enter o or o as appropriate If the limit does not otherwise exist enter DNE c d lim f x x 20 lim x lim f x KIL lim f x X 3 4 2 21 4 6 c the equations of the asymptotes Enter your answers as comma separated lists X G D

ify the intercepts Ay 6 4 2 2 o o Select the correct choice below and if necessary fill in the answer box to complete your choice AL x intercept s 5 0 5 0 Type an ordered pair Use a comma to separate answers as needed B There is no x intercept Select the correct choice below and if necessary fill in the answer box to complete your choice OA y intercept s Type an ordered pair Use a comma to separate answers as needed OB There is no y intercept

6 6 points Let A be a 3 x 4 matrix whose null space is 1 2 X t tER 3 4 N A a Determine the rank of A b Find the range of A 3 A 0 1 c Is the vector in the row space of A State also the reason

d the slope of the line if it exists 0 10 Ay Q G Select the correct choice below and if necessary fill in the answer box to complete yo A The slope is Type an integer or a simplified fraction B The slope is undefined

For the equation find three ordered pair solutions by completing the table Then use any two of the ordered pairs to graph the equation Complete the table below X 10 10 8

Ing by plotting po For the following equation find three ordered pair solutions by completing the table Then use the ordered pairs to graph the equation y 2x 1 Find three ordered pair solutions of the given equation X 0 1 y 1 Part 2 of 4 10 O Points 0 of 1 AY G

B A 20 B 60 A 20 60 20 1100 7001 110 2 D 40 D 50 NIS 84715810 30 30 50 C

Find seven ordered pairs to the equation y x 9 Then determine its graph 1 X 3 y 0

The value of 5 04 O 3 O O 01 5 151 in U is

the measure of Arc AC 80 what is m B B

decreasing constant Question 39 Determine the increasing decreasing and constant intervals if they exist If and interval does not exist enter in NA Use inf to represent oo and u represent oo Use U if an interval has more than one solution 3 3 Increasing 3 1 Decreasing 3 3 3 1

2 Letj R R be continuous and g a b R be absolutely continuous a Sow that the function is absolutely continuous b Find for almost all re a b F x f t dt

Find C in degrees C B a C a 10 b 7 c 6 C degrees Round to the nearest tenth

The graph of h x is shown 6 5 h x 4 3 7 6 5 4 3 2 1 2 1 0 y 2 3 Y 5 6 1 2 3 4 5 6 7

A matrix A has the following eigenpairs A 3 5 2 Use these eigenpairs to find matrix A Hint A PDP A 1 1 11 Ex 5

domain range 5 4 3 d 2 1 f 3 10 A 1 3 2 1 1 2 3 4 5 6 Use the graph to find the indicated function values a f 3 b f 2 c f 0 1 2 y f x 3 4 5 X

a c 20 we have 5 0 3 1 13 1 HR 1111 1 1 2 2 1611 1 2 1 1 5 0 d 12 1 1 3 5 1611 0 1 13 2 5 0

A 37 inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece is two inches more than four times the length of the first piece Find the lengths of the pieces What is the length of the first piece 5 in What is the length of the second piece BOCCHA 2x 2 4x

Use the graph of f to determine each of the following Where applicable use interval notation a the domain of f b the range of f c the number at which f has a relative minimum d the relative minimum of f a What is the domain of f Use interval notation b What is the range of f Use interval notation c What is the number at which f has a relative minimum d What is the relative minimum of f 61 11 2 X 4 6 8 10

Let a b and C be real numbers with a 0 Match each equation or expression to its appropriate name Drag a response from the right column up or down until it aligns with its match in the left column and drop it Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Standard form of a quadratic equation Discriminant of a quadratic equation Quadratic formula III III ax bx c 0 x k ax b c b 4ac

1 21x 15y 2 14c 2c 3 5P 129 Factor the following difference of Squares for 7 7 0 64 8 Y 289 GCF for 1 3 9 m 81

3 Use the following table to solve the equations below 2 11 6 4 X f x 3x 5 g x 2x 7 m x 3x 2 a 3x 3 2 b g x 10 c 3 3 1 3x 5 2x 7 1 8 8 1 0 5 10 2 d m x 4 e 3x 2 1 1 2 12 5 the total alahal rafuose nonulation under the mandate of the UN Refugee Agency Give the domain Range for for f x

1 Find the length of c A a 8 b 7 c units Round to the nearest tenth Ent

Select all intervals where f x 0 and f x 0 y f x JJ Select one O a 5 3 U 3 5 O b 1 3 O c 3 1 d 11 2 3 N

Let sino 3 20 8 the exact values of the five remaining trig functions of 0 where cat 70 Find

The bar graph shows the number of fatal vehicle crashes per 100 million miles driven for drivers of various age groups The number of fatal vehicle crashes per 100 million miles N for drivers of age x can be modeled by the following formula N 0 014x 1 21x 28 23 Fatalities 100 Million Miles 18 12 64 According to the formula what age groups are expected to be involved in 4 fatal crashes per 100 million miles driven year olds Round to the nearest integer Use a comma to separate answers as needed 12 5 16 Age of Drivers and Fatal Crashes 11 0 18 9 6 20 6 7 3 0 2 1 4 0 8 7 16 2 20 25 35 45 55 65 75 79 Age of Drivers

Find the area of this triangle if C radians a 57 and b 8 9 7 T A A B a C square units Round to the nearest tenth C b Enter

Identify a basis for the following subspace a a b 2b 3a W 1 1 2 A 23 ER2x2 a b ER is a subset of R2x2 11 0 1 23 B 20 1 1 23 2 3

Price 14 12 LO 8 6 4 2 Price of Lemons 2 4 6 8 10 12 14 Number of Lemons Find the unit rate of the price per lemon 3 4 lemons 1 lemon Give your answer as a decimal Enter

Consider the following figure 6 2 2 Match the statement of the limit with actual limit lim f x x 3 lim f x x 3 lim f x X 3 f 3 y f x 2 7 A 1 B 2 C DNE D 1

x 3 y uppose that x y 1 2 2 1 Then the configuration 6 754 8 can be 1 2 3 eached from the 8 puzzle 4 5 6 by moving squares in and out of the space 17 9

a Calculate the volume of a sphere of radius r 2 with Riemann Sums when n 4 and the sample points are the midpoints x7 Show your work 5 points

1 Simplify with only positive exponents 4 y xz 3 xy z

Find the domain and range of f x 2 x 4

Mr Green orders some cookies from a local youth group Using his order form shown below complete the last column find the total to be paid a b C Quantity 1 2 1 9 54 12 26 12 90 19 64 Description Krispy Kosmos Chewy Chocos Gooey Globs Unit Price 2 89 3 19 2 99 Total 5 2 tax Total to be paid Total of Line 55 6969 555

a Let an be an arithmetic sequence If a6 38 a11 b Consider the geometric series 405 135 8 Otherwise state the reason why the series is divergent 1215 32 16 73 find the common difference d and the formula for an 45 4 15 Find the exact sum of the geometric series if possible 2

1 4 To calculate tax on 63 78 multiply 4 2 times 63 78 5 Please select the best answer from the choices provided

7 Rounded to the nearest thousandth what is the decimal equivalent of 6 a 0 067 b 0 068 C 0 677 d 0 678 Please select the best answer from the choices provided

Name 82 Explain the two transformations that cou

4 Determine the domain of the function f x 2x 10 Explain or show how you arrived at your answer

In R the vector a True b False H 6 8 4D is in the span of

Question 35 Given the trigonometric function defined by f x 3 sin 6x 1 What is the amplitude of the function 3 2 What is the period of the function 3 Sketch one period of the function 5 12 Clear All Draw M 3 3 2 AN 3 JU4 J12 2 3 5 4 J 12 JU4 fd3

53 A sequence is defined by the rule a i a with a 4 Determine the value of a4 a jolorit 20 naidw ove 1 pi

Match each inequality with the interval notation that represents its solution set Drag the response from the right column up or down until it aligns with the correct match from the left column Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE X 50 x2 50 x 50 0 50 0 50 E 50 00

The table below shows the typical hours worked by employees at a company salary of 37 000 Hourly employees get paid 14 per hour but get 21 per hour for each hour over 40 hours Should new employee is offered an annual the new employee choose the salaried or hourly pay Explain your reasoning Tues Wed Thurs Sun 0 Mon 8 5 9 5 7 5 8 Fri 8 5 Sat 4