Sequences & Series Questions and Answers

Click on the graph of x 4 A B C D H G

The point a 2 5 No answer given on the line with vector equation The points on that is closest to a is and the distance between the point a and the line is 13 X 5 7 t 2 1

The length of a petal on a certain flower varies from 3 61 cm to 8 41 cm and has a probability density function defined by f x length of a randomly selected petal will be as follows a Greater than or equal to 3 8 cm b Less than or equal to 3 7 cm c Between 3 7 cm and 3 8 cm a The probability that the length of a randomly selected petal is greater than or equal to 3 8 cm is b The probability that the length of a randomly selected petal is less than or equal to 3 7 cm is c The probability that the length of a randomly selected petal is between 3 7 cm and 3 8 cm is 1 24 x Find the probabilities that the Round to four decimal places as needed Round to four decimal places as needed Round to four decimal places as needed j

Type your X X a f 2 Use the function f x 6 2 4 to fill in the blanks with the appropriate information b f 3 c f 0 sin all of the blanks and submit e Range of f 2 Type your answer here Type your answer here d Domain off Type your answer here Write your response here Mirite your response here Round to three decimal places Enter the domain in interval notation Enter the range in interval notation f Horizontal asymptote RICE PUTEBOOnse here Enter the equation with no spaces K

Type your answers in all of the blanks and submit X X 2 Fill in each blank with the appropriate information a The graph of the function f x 3 b The graph of the function f x e is c The number e is a n Type your answer here X is Write your response here Write your response here Write your response here increasing or decreasing over its domain Round to three decimal places increasing or decreasing over its domain rational or irrational number whose approximate value is

Type your answers in all of the blanks and submit X X Use the function to fill in the blanks with the appropriate information f x 4 a f 1 b f 0 c f 1 2 e Range off d Domain off Write your response here Type your answer here Type your answer here Write your response here Write your response rere f Horizontal asymptote Enter the decimal form of the number Enter the domain in interval notation Enter infinity or infinity as needed Enter the range in interval notation Enter infinity or infinity as needed ce your response here Enter the equation with no spaces

Graph the function f x cos x 4 over the interval 0 2x Partition the interval into 4 subintervals of equal length Then add to your sketch the rectangles associated 4 with the Riemann sum f x Axk using the left endpoint in the kth subinterval for C k 1 2x OA O C Im me fill in G 2it CIT OB G OD

8 Problem 12 Let f x x 5 and g x a Evaluate fog 1 x 1 7 point

The graph of the function y 2 is shown Click where the five specific points on the graph of y 2 will move to obtain the graph of the function f x 2x 3 1 using transformations

2 a Find all positive integers n such that n 2 10 mod 3 b Let p 3 5 7 be a prime Prove that there are infinitely many integers n satisfying the congruen n 315 2022 0 mod p

X Use the function to fill in the blanks with the appropriate information f x X 2 b f 0 a f 1 4 c f 1 d f 3 X f Range off Write your response here Type your answer here e Domain off Write your response here Type your answer here Write your response mere rice your response mere Enter the domain in interval notation Enter infinity or infinity as needed Enter the range in interval notation Enter infinity or infinity as needed g Horizontal asymptote WICE CESCOTSE TEE Enter the equation with no spaces

2 Write an equation for the perimeter P of each figure as a function of side x Describe the domain and the range a x b x 7 The images are not to scale

c Use S Pert to find the future value of 7 500 invested for 4 years at 2 5 compounded continuously Fill in the formula Label your answer and round it to two decimal places P r 2 5 t S decimal

Suppose that a n 1 is a sequence defined by a 1 a 3 and a a a 2 Vk 3 7 Prove that Vn21 we have a

Find the logarithm using the change of base formula log 10 log 710 Round to four decimal places as needec

Find the values of x y and z in the figure where a 2 and b 4 X O y Z O Do 01 ax b ax b

a Show that if f x has a finite jump discontinuity at x a then F f x AF w B f a f a eiwa in which F stands for the Fourier Transform and A and B are constants Also f A and B b Find the Fourier Transform of f x if f x x if 0 x 1 0 otherwise

Express as a single logarithm and if possible simplify 1 2 log b 5log c 1 2 Use parentheses to indicate the argument of the logarithm log b 5 log c

Find the inverse function for f x 5x 3 x x 3 1 0 1 5 x 3 5x 3 5x 3 35 1 5x 3 5x 3

Given that log x 2 log ay 3 and log az 4 find the following 4 4 6 y z log log 2 3 X Z 46 a 4 2 3 II Simplify your answer Type an integer or a fraction

The graph of a function f is given Use the graph to solve f x 0 Enter the solution set in interval notation below 3 5 4 3 2 1 1 2 4

1 Given that log 4 1 386 log 8 2 079 and log 12 2 485 find the logarithm of log b 32 log b 32 Simplify your answer Round to the nearest thousandth

If 7000 is invested for t years at 7 interest compounded continuously the future value is given by S 7000 e 0 07t a Graph this function for 0 st 15 Choose the correct graph below A 34 000 AS 0 0 15 OB AS 34 000 0 0 18 651 19 Round to the nearest whole number as needed 15 C 34 000 AS 0 0 15 G b Use the graph to estimate when the future value will be 16 000 Choose the correct answer below A t 10 81 years OB t 23 62 years C t 11 81 years c Complete the following table t Year S dollars Complete parts a through c O D AS 34 000 0 15 OD t 12 81 years

Given that log x 2 log y 3 and log z 4 find the following log 4 4 6 y4z6 4x z A y z log a 4 2 3 X Z Simplify your answer Type an integer or a fraction

92 voters are asked to rank four brands of cereal A B C and D The votes are summarized in the preference table shown below Determine the winner using the plurality with elimination method 43 31 11 3 D A B C A B C D B C A A C D 0 B Number of Votes First Choice Second Choice Third Choice Fourth Choice Select the winner below 00 OD A

For each linear transformation below state a basis for Ker T the Nullity of the transformation and the Rank of the transformation If you do not need a vector then place zeros for all entries of that vector for example if you only need 2 vectors for the basis then fill in the first two vectors and make all subsequent vectors have 0 for all boxes 1 Let T la 1 b 0c la 0b 0c 2a 1 b 0c 4a 1 b 0c A basis for Ker T would be i The Nullity of Tis i The Rank of Tis

A graphing calculator is recommended Graph the functions on the same screen using the given viewing rectangle Viewing rectangle 8 8 by 2 8 a y x b c y 2 x 5 y x 5 d 5

1 The diagram shows a rhombus ABCD BE is an extension of AB such that AB BE 4 3 and point F is the midpoint of CD Find an expression for the vector FE in terms of a and b D A olvo O a C B b E

Find the critical value to for the confidence level c 0 99 and sample size n 6 to 11 Click the icon to view the t distribution table Round to the nearest thousandth as needed

Suppose a primitive economy consists of two industries farm products and farm machinery Suppose also that its technology matrix is represented matrix shown below by the A P products M 0 6 0 2 0 2 0 4 units Products If surpluses of 95 units of farm products and 7 units of farm machinery are desired find the gross production of each industry Machinery

Consider the quadratic sequence T 8 10 10 that is this should be viewed as a sequence T an a Find the nth term for this sequence T b What is the value of T4 T bn c for some constants a b and c c Suppose the difference between two consecutive terms in this sequence is 18 Find the values of these terms i e list the two terms in order

Let A 1 2 3 4 5 6 7 B 4 5 6 7 8 9 10 C 2 4 6 8 10 anc U x xel 0 x 10 1 Find each set a C A b ANBNCI C AUC B BOC

Find the position vector v that corresponds to the vector graphed below Note that each box in the grid is 1 unit by 1 unit in size 3 2 3 2 a Vector with initial point 3 2 and terminal point 3 2 Type your answer in component form a b where a and b represent some numbers Use the and keys SHIFT and SHIFT that are located below the L key on your computer s keyboard for the brackets in component form

A highway whose primary directions are north south is being constructed along the west coast of a region At one point a bay obstructs the straight path of the road Since the cost of a bridge is prohibitive engineers decide to go around the bay The figure shows a diagram of the path that they decide on and the measurements taken If L 5 mi what is the length of highway needed to go around the bay Bay 140 B 135 E D 1 8 mi C 1 8 mi The total length of the highway needed to go around the bay is about miles Do not round until the final answer Then round to two decimal places as needed

Write an equation for the graph below in terms of 5 3 2 y 3 2 1 2 3 4 5 d

7 Verify the identity 2 csc A sin A 1 cos A 1 cos A sin A

of the following graphs show a function which is one to one Select all correct answers Select all that apply T

1 Determine whether the following series are convergent or divergent Justify your answers including which test method you use En 1 n 1

Verify the identity cos 24 1 sin 24 cot A 1 cot A 1

Here is the graph of 3 cos 2 A B C 23 over the interval Give the coordinates of point A the y intercept Give the coordinates of point B the first z intercept along the positive z axis Give the coordinates of point C the first peak of the graph with positive z value

for r 3 r 4 c Using your results from b find Question 2 7 marks nty r 3 r 4 77 1 3 4x x 3 a Use the factorial definition of to show that b Using the result from a find another way to write c Using the result from b find az such that 13 2 marks 2 marks 1 marks 4 marks

the distances between your apartment A and the places you must visit to complete your chores Assume all blocks are the same length Find a Hamilton circuit using the nearest neighbor algorithm State the weight of your path E Campus Security D Student C Library Center A Apartment B Advisor

Use an identity to write the expression as a single trigonometric function value or as a single number 1 1 8 4 sin 71 7

Let f be the exponential function defined by and determine the following information based on f Horizontal Asymptote 4 Range intercept v Letter Comesponding to Graph HE A a 10 2 B TIT D

Use the given measurements to solve the triangle Round lengths of sides to the nearest tenth and angle measures to the nearest degree a 600 b 500 The measure of angle B is approximately Round to the nearest degree KOD B

3 students from an astronomy class Student Number of Absences Final Grade percent 79 78 86 56 75 1 2 3 4 S 6 7 8 19 10 11 12 13 14 15 E 5 6 2 12 D 19 15 8 15 0 1 9 80 13 The linear regression line is 10 3 11 yax b y 72x 853 y 94 255 R F 5 90 78 48 92 78 81 96 75 89 65 45 T G MacBook Pro A 6 A Y 7 H 8 8 J 1 t 9 K

Exercise 4 1 pts For ne N let P be a probability on 2 4 Consider a sequence of real numbers 0 neN satisfying an 20 for ne N and E 10 1 Show that P A 1kPn A is a probability on n A

Write an equation for the polynomial graphed below 5 y x 3 2 6 5 4 3 2 1 2 3444 3 5 6 2 4 5 a

Write the equation of the line whose graph is given The correct equation is Simplify your answer Ay

Consider the following figure Find EC B EC D Given Find A E C Write a proportion involving EC that can be used to solve for EC 5 13 DE 1 BC AD 5 DB 13 AE 7 EC