Sequences & Series Questions and Answers

Determine whether the function is or is not periodic If it is find the period Ay 8 4 Select the correct choice below and fill in any answer boxes within your choice OA The function is periodic The period is OB The function is not periodic

Given the Venn diagram below Qu Q 3 1 A 2 8 7 20 6 12 5 15 B 10 C Find the elements of the following sets Q 3 1 1 A Q 3 1 2 B Q 3 1 3 C Q 3 1 4 AUB Q 3 1 5 The universal set a 13 14 11 3 13 2 3 2

the range of the given graph Select one Oa 0 O b 6 OC 0 6 d 0 BA SH 144 0 1 0 1

Use the table below to fill in the missing values 0 1 234567 8 9 We 0 4 if f x 857 2 3 1 9 6 f 1 if f x 9 then x 4 8 then r

ential thmic ons 4 nces 4 Describe any phase shift and vertical shift in the graph a y 3 sin x 1 b y sin x sin x 11 2 2

d 2 y x 5 x 1 y x 3 x 1 5 5 5 5

4 Identify the period for the tangent function then sketch a graph by hand and upload a photo 2 3 e y tan

a b Find the exact values of the cosine and sine of each angle Then find the decimal values to the nearest hundre c 390 4208 60 390

In the diagram below MN is parallel to JK If ML 2 4 JK 2 4 JK 3 LK 2 and MN 1 8 find the length of JL Figures are not necessarily drawn to scale M N L K

nvert to an exponential equation log V The equivalent equation is Type in exponential form

Find the logarithm using the change of base formula log590 log590 Simplify your answer Type an integer or a decimal Round to fou decimal places as needed

7 For the function f x cos 2x 0 1 x 6 find the positions of any local minima or maxima and distinguish between them

3 Use a graphing calculator to graph the function y tan x from 0 x 2m and 200 y 200 Evaluate the function at a 4 b 2

3 Complete the chart in your notes Save for future reference Quadrant II cosis sinis Quadrant III cosis sinis Quadrant I cosis sinis X Quadrant IV cos is sin is a If cosine is positive and sine is negative in which quadrant is the terminal side of the angle b If cosine is negative and sine is negative in which quadrant is the terminal side of the angle c Explain how the mnemonic device All students take Calculus can help you with the chart Reminder tan

Use logarithms to find x in terms of x y 10x 10 X 2

1 In 1915 the tallest flagpole in the world stood in San Francisco 210 ft a When the angle of elevation of the sun was 55 degrees the length of the shadow cast by this flagpole was 210 ft Find the height c lagpole to the nearest foot Show your work

An ice skating rink charges an admission fee of 5 for members and 10 for nonmembers Last Saturday the number of members was at least twice the number of nonmembers The rink had collected at most 300 in admissions If m is the number of members and n is the number of nonmembers which graph represents the possible solutions for the number of each kind of skater O n nonmembers n nonmembers y 50 S 40 30 20 10 O y 50 40 30 20 10 O 50 40 30 15 10 20 30 40 50 60 m members 30 15 70 10 20 30 40 50 60 70 m members X

Determine the Interval where the function is increasing 43 Oa 2 00 Ob 2 00 Oc 00 2 Od 0 2 24 RA

What is the domain of the given graph 3 Select one O a 1 Ob 1 OC 1 00 D D 1 5

Find f 2 for the function f x f 2 fr 1 if I 2 31 9 if I 2

3 Find the period of each curve then write an equation for each sine functic a W b nuov A

Find f 4 for the function 15 if if f x 2x 3 11 f 4 4 4 3 if 123

35 Let a be the rule that assigns to each English word the first letter in the word Find a a bicycle b a porcupine and c a plastic

Find the range of the following graph 2 Select one Oa 0 5 O b 0 OC 0 00 Od 1 0 0 6 34 PA 0 10 E 3 31

Find the characteristic polynomial for the matrix 12 1 10 3 A A 2 X 1 x 1 B A 2 A 1 x 1 C A 2 x 1 D A 2 A 1 E A 2

Graph the line with slope 44 passing through the point 3 3 19 X

In the figure below O is the center of the circle Find each measurement below 330 a mZACO b mAC c mCB d mAB e mCBA 57 660 0 57 B

14 The table and graph below shows the number of minutes left on your cell phone plan over the course of the month Predict the number of minutes left on your cell phone on the eighth of the month according to the prediction line Day Minutes 2 5 7 14 15 18 Minutes Remaining 50 45 40 35 30 25 20 15 10 5 34 30 22 20 10 5

Below is a graph of y g z which is a transformation of the graph f x I Which function for g best matches the graph Og z 2 24 Og z 2 64 Og z 2 37 Og z I 42 9 2 2 16 g z 35 T

Problem 11 5 2 7 points It is given that for n 0 an 1 bn 1 an and ao 1 bo 2 a Find explicit formulas for an bn b Find limn 3an 40 6am 70

Determine whether the data show a linear relationship by plotting the points and drawing the line If so write an equation of a line of fit Estimate y when x 15 and explain its meaning in context Hours x Battery life y OA yes y 100x 5 y 1495 After 15 hours the battery will have 1495 left 1 95 7 65 5 12 39 7 OB no C yes y 5x 100 y 25 After 15 hours the battery will have 25 left D yes y 5x 100 y 25 After 15 hours the battery will have 25 left 16 20 9 21 5

Find the sizes of all the angles in degrees and sides in meters of shapes that are similar to the given parallelogram with the given scale fact a 6 1 b 115 longer side 0 7 shorter side 0 3 larger angle 115 smaller angle 65 longer side shorter side larger angle smaller angle 7 m X m X m EE 0 3 m O 0033

Characteristics of Comp Counselors Grade Level Male Female 21 16 Junior Senior 18 25 Find P counselor a junior counselor female Write your answer as a fraction in simplest form a b

The orbit of a point P is defined by the following function Tp t y t sin x p t cos 60 x t What is the smallest value for p 60 for which the period of the lissajous figure equals

Write the expression as a single term factored completely Do not rationalize the denominator Ilz Select one 145 vilz b C Od 9 85 Sylla 9 M Wilz 945r Buite X

Conside following figure Note that the figure is not drawn to scale 83 Sa 50 Order the side lengths EF FH EG FG and HG from least to greatest

Use integration by substitution to find the indefinite integral in part a and to evaluate to 2 d p the definite integral in part b a b 3x 2 2x 4x dx 3t e t 1 dt

Fill in the blanks to complete the square and make a perfect square trinomial b For x 6x a For x 4x x 4x x 4x x 6x x 6x c For x 8x 11 1 3 x 8x x 8x

Determine the period of the function 12 AD 12 Q S

Without using a calculator determine the graph of f x x 4 Click on the center of the correct graph mi D

Find the a b c indicated values for f x 2X f 0 1 24 1 24 a f 0 b 1 24 c f 24

An administrative secretary eams 15 per hour up to 40 hours in a week The time that the admin works over 40 hours in a week is paid at time and a half What is the piecewise defined function that models the total weekly earnings for X hours of work Select an answer and submit For keyboard navigation use the up down arrow keys to select an answer 06 f x b f x c f x f x 15x 15x22 5x 15x If 0 x 40 if x 40 15x 15x 22 5 x 40 if x 40 600 22 5x if 0 x 40 if 0 x 40 if x 40 15x 600 22 5 x 40 if 0 x 40 if x 40 ISLAHI

100 50 What is the maximum height the ball reaches When does the ball reach it s maximum height after A When does the ball hit the ground seconds 7 0 8 meters 5 2 round all answers to the nearest tenth A tennis ball is thrown straight up with an initial vertical velocity of 49 6 m s from an initial height o meters Use the Desmos graph above to answer the questions below seconds 9 6 3 ans

O O 13 1 cm 9 2 cm 7 1 cm 8 4 cm 40 11 cm X

1 point Consider the graph of the function f x shown below Click on the graph for a larger version A Estimate the integral f f x dx B If F is an antiderivative of the same function f and F 0 35 estimate F 7 F 7

Expand sin 1 j and show it on the Argand Diagra

Click on the center of the graph that best matches the graph of the function g x x 20 80 C

Suppose that f x log 3x a What is f 9 What point is on the graph of f2 b If f x 1 what is x What point is on the graph of f

Find the vertical asymptotes for the function f x 2 2 2 3 2 6 Select one or more ay 0 b c x 6 x 6 Od y 3 O e x 3 Of y 2 O g x 3

B Does the series n 1 n 2n 1 converge