Sequences & Series Questions and Answers

and determine the following information based on f i Horizontal Asymptote ii Range iii y intercept iv Letter Corresponding to Graph 1 point 5 4 4 f x A x 5 B M

Following is the graph of f x x Describe the vertical horizontal translations and the vertical stretch or compression and sketch the graph y g x 3 x 2 1 Label the new positions of points A B and C after the translation on the graph of y g x A 1 1 B 0 0 C 1 1

The Mos Body Surfase is B hw where B is an 3131 individual s Body surface area in square meters h is the individna is height in inches and w is the individual s weight in pounds Find The Body Surface OF an individual who is 55 inches tall and who weighs 139 pounds avec The Body of the individual is 1

Use then of the function y h x below to answer the questi 3 s W 3 5 a Is h 5 positive Yes No b For which value s of x is h x 0 If there is more than one value separate them with commas c For which varie s of x is h x 0 Write your answer using interval notation

Graph f x 3 and g x log 3x in the same rectangular coordinate system Choose the correct graph below Ay 10 G

S y varies at a constant rate of change of 5 with respect to z so that Ay 5 Az and when z 2 y a If z varies from z 2 to z 7 the change in z is Az 5 Preview b If z varies from z 2 to z 7 the change in y is Ay c What is the value of y when z 7 Preview 5 5 www

Evaluate or simplify the expression without using a calculator In e 2x 2x

Find two negative and three positive angles expressed in radians for which the point on the unit circle that corresponds to each angle is Choose the correct angles below O A OB O C O D 14x 3 18x 5 T 10x 8 2 8 3 3 3 2 5 3 3 3 1 4 2 8 18 5 5 5 10x 4 2 4 14 3 3 2 14x 3 2 8 14x 7 NI 2

t the matrix 2 1 act on C Find the eigenvalues and a basis for each eigenspace in C 4 37 lect all that apply A 6 3i v C 3 6i v E 3 6i v G 3 6i v 1 6i 37 1 6i 3 1 6i 3 1 6i 37 C 0 v 1 06 B 3 6 i v D 3 6 i v F 6 3i v H 3 6 i v 1 6i 37 1 6 i 37 1 6i 6

mplete a and b You can verify your conclusions by graphing the functions with a graphing calculator 6x lim 4x x x 2 a Use analytic methods to evaluate the limit If the limit is infinite enter or as appropriate If the limit does not otherwise exist enter DN b What does the result from part a tell you about horizontal asymptotes O The result does not yield any information regarding horizontal asymptotes O The result indicates that there are no horizontal asymptotes O The result indicates that there is a horizontal asymptote

The following four statements are true about the graph of the rational function T As T 00 y 30 As 0 y 30 As I 18 y 0 As I 18 y The function that is described here could be Oa r I 7 18 30 1 Ob r t z 18 30 Ocr x 1 z 18 30 Od r x 18 30 I 18

Evaluate the expression without using a calculator 1 log 55

The function s t 16t2 64t 100 models a ball s height in feet above the ground t seconds after the ball is thrown vertically upward Find the maximum height attained by the ball The maximum height is A feet above the ground

Use the graphs of f and g to answer the questions below The magenta graph is y f z The blue graph is y g z Part 1 Part 2 V NH B x 333 12345 Part 4 styny f g 3 42 f g 6 Part 3 fg 6

Juniors Seniors Total Gym equipment 240 Computers Total 540 300 160 460 rincipal of a school is deciding whether to spend a budget surplus on new gym equipment or computers ncomplete table above summarizes the preferences among junior and senior class students If a senior How the school is chosen at random the probability that the student prefers gym equipment is 1 3 y seniors are at the school

Write the following equation in its equivalent logarithmic form 16 4 The equation in logarithmic form is Type an equation

The graph of y x 20 45 is the graph of y shifted how C State the direction of each shift followed by the number of units of that shift up down and right left A units P N

Choose the best matching graph based on the description of a polynomial The polynomial function has the following properties The leading coefficient is negative The degree is odd It has a zero at x A with a multiplicity that is even Which graph best matches the description of the polynomial function A m Wil A

5 a 15 pts Determine what the Fourier cosine series of the function 2 3 for 0 x 1 for 1 x 4 4 converges to at all points of the interval of definition

For the function f defined by f x 5x 3 complete the tables below for f and f 1 Complete the table on the right THE X 4 3 2 1 0 f x 23 X 23 18 13 8 3 f 1 x

Determine the total surface area of an octahedron whose edges have a length of x O O O O O8x 2 O 2 3 x 2 3 x 2 O 2 5 x 2 O

4 If sin following a b and terminates in Quadrant III find the exact value of each of the 5 sin 20 COS

What is the area of a circle inscribed in a triangle whose sides a b and c are 8 12 and 6 respectively units O 1 4 sq units O 1 5 sq units O 1 6 sq units 1 7 sq units

Is the function shown on the graph below one to one X N OYE

Someone has been using the following nonstandard units in finding the areas of regions Unit P Unit Q a Tell whether x or 90 is greater and explain 90 P s x R s 90 x because unit P is b Tell which of y or x is greater and explain y Q s x R s x because unit Q is v than unit R c If 22 P s 7 Q s how many P s make 1 Q 0 318 X P s Unit R than unit R If 22 P s 7 Q s how many Q s make 1 P 0 318 X Q s How many globs make 1 blob 106420 d If 3 5 blobs 2 2 globs then how many blobs make 1 glob 1 59 X blobs

Compute the following radical 81 A 7 B 8 C 9 D 10

Use the matrices below to perform the indicated operations A 27 2 B 1 1 AB 8 3 88 TIP

Plot the point s where tan 0 0

Let A x f t dt with f x shown in the graph below 5 4 3 2 1 W 2 3 T 5 My 3 4 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6 ur

Exercise 2 Solve the optimal control problem Answer max j 20 2y t u t dt y t u t 2y t y 0 1 y 1 free

Solve for x A 40 B 20 C 55 OD 35 60 2x 20

Find the amplitudo the period any vertical translation and any phase shift of the graph of the following function y 5sin What is the amplitude of the function 5 Type an integer or a simplified fraction What is the period of the function Simplify your answer Tyne an vart answer using as needed Ise inteners or fractions for any numbers in the expressi

COS B 2 given sin 3 1 B T 7 E 5 2

1 Let f x 6x 5 and g x Find f g x f g x fg x and X 1 f g x 6x 5 Simplify your answer X f g x fg x x 6x 5 1 X 6x 5 X Simplify your answer Simplify your answer x Simplify your answer x Give the domain of each

For the function f x x 4x 6 complete parts a through c a f x h x 2xh h 4x 4h 6 Simplify your answer b f x h f x h 2xh 4h Simplify your answer f x h f x h c 11 Simplify your answer

Let 4 x f t dt with f x shown in the graph below 5 4 3 2 1 1 3 At what x values does A x have a local max x At what x values does A x have a local min x Restrict your answers to values 0 x 6 5 Ta

1 The following table shows the number in millions of cars sold in the U S years after 2005 Use the regression line for the data to estimate the number of cars sold in 2013 t C A 3 70 million B 4 92 million C 3 16 million D 4 07 million 0 5 54 1 5 46 3 5 24 5 4 54

Identify the radicand in the radical below 3 3x 5 A 2 B 3 C 5 D 3x 5

X 6 Use f x 2x and g x to evaluate the expression 2 a fog 4 b gof 6 a fog 4 2 Simplify your answer b gof 6 Simplify your answer

of the polar equal coordinates Then identify and graph the equation Write an equation in rectangular coordinates Type an equation What is the graph of this equation O A horizontal line OC vertical line Select the graph of r 2 cos 0 O A Q in rectangular B r 2 cos 0 OB circle with center at 1 0 OD circle with center at 1 0 OC O D

a Find the slope of the line and b interpret the slope Simplify your answer a The slope of the line is b Interpret the slope For every 5 unit change in x the change in y is SCLER unit s Simplify your answer 53 21 Q

The Richter Scale reading of an earthquake is based on a logarithmic equation Suppose R log 4 where A the measure of the amplitude of the earthquake wave Ao the amplitude of the smallest detectable wave or standard wave An earthquake is measured with a wave amplitude A 0 4471 while the smallest detectable wave Ao is measured at 0 0001 cm What is the magnitude of this earthquake using the Richter scale to the nearest tenth The earthquake registered 8 3 x on the Richter scale

Let f x 6x 5 and g x f g x fg x 1 f g x 6x 5 Simplify your answer X 4 X16X 5 1 X 6x 5 X X Find f g x f g x fg x and Simplify your answer Simplify your answer x x 6x 5 Simplify your answer The domain of f g is Type your answer in interval notation x Give the domain of each

Find fog x and gof x 8 f x 4x 7 g x 256 x 2 Simplify your answer Do not factor gof x fog x x co 7

Find a basis for S for the subspace S 1 1 6 S span 4

1 Let f x 6x 5 and g x Find f g x f g x fg x and X f g x 6x 5 X f g x fg x 6 x 6x 5 1 X 6x 5 X Simplify your answer Simplify your answer Simplify your answer x x 6x 5 Simplify your answer The domain of f g is 5 6 Type your answer in interval notation The domain off g is Type your answer in interval notation x Give the domain of each

13 Use the Five Point Method for graphing one period of the following function y 3 sin 2 x

Match each description of a graph to its end behavior using arrow notation Drag and drop options on the right hand side and submit For keyboard navigation SHOW MORE Asx oo y 0 As x xo y x Asxxy 00 As x y x Up to the right Down to the right Up to the left Down to the left

Find an equation for the line which is perpendicular to both the lines through their intersection point Equation 8 0 0 0 0 0 0 t and which passes

onsider the following figure TN R 30 Given Find M N T 14 S ARST with right ZRST mzR 30 and ST 14 ZRST is trisected by SM and SN TN NM and MR