Questions

lim sin x 4 sin 4 2 0 sin x 4 O sin x cos 4 cos x sin 4 sin a sin 4 cos x cos 4 sin a sin 4 cos x cos 4 sin x cos 4 cos x sin 4 W So sin 4 sin 4 sin z cos 4 sin 4 cos x 1 sin x cos 4 cos z sin r sin x 4 sin 4 So 0 0 sin z cos 4 sin 4 cos z 1 H sin 4 sin 4 A sin z 4 sin 4 lim 2 0 sin z cos 4 lim 0 Part 2 of Part 3 of 5 Part 4 of 5 Part 5 of 5 sin 4 cos z 1

Consider the cost function C x 7x2 12x 24 thousand dollars a What is the marginal cost at production level x 5 b Use the marginal cost at x 5 to estimate the cost of producing 5 50 units c Let R x x 41x 36 denote the revenue in thousands of dollars generated from the production of x units What is the break even point Recall that the break even point is when the revenue is equal to the cost d Compute and compare the marginal revenue and marginal cost at the break even point Should the company increase production beyond the break even point a The marginal cost at production level x 5 is C

Ay 01 0 3 0 y f t y f t 10 12 14 16 8 Years after 1980 Q OU Q ndituror in billions of dollars The red Next question National health expend dollars from 1980 to 1994 are given by the function f t in the graph to the left a How much money was being spent at the beginning of 1983 billion

The graph of y f x solid and y g x dashed is shown 6 5 4 3 4 lim 2 1 9 x 0 8 f x lim 24 1 g z Does Not Exist 88 0 8 2 z 1 g z Does Not Exist 0 Find the following limits 1 Does Not Exist 6 5 4 3 2 1 2 3 nd 5 6 2 3 4 1 1 1 1 S 6 q

Let f t be the temperature of a cup of coffee t minutes after it has been poured Interpret f 8 110 and f 8 5 Estimate the temperature of the coffee after 8 minutes and 42 seconds that is after 8 7 minutes C What does f 8 110 imply OA 8 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 110 degrees per minute B 110 minutes after the coffee has been poured the temperature of the cup of coffee is 8 degrees O C 110 minutes after the coffee has been poured the temperature of the cup of coffee is rising at a rate of 8 degrees per minute OD 8 minutes after the coffee has been poured the temperature of the cup of coffee is 110 degrees

What is the surface area of the right cone below 13 14 OA 104 units O B 54 units OC 68 units PREVIOUS

An analysis of the daily output of a factory assembly line shows that about 70t t At t 6 the rate of production is units per hour 1 t3 units are produced after t hours of work 0 st 8 What is the rate of production in units per hour when t 62 108 CL

Suppose that f x x a What is the average rate of change of f x over each of the following intervals 3 to 4 3 to 3 5 3 and to 3 1 b What is the instantaneous rate of change of f x when x 3 a The average rate of change of f x over the interval 3 to 4 is Simplify your answer

Which of the following is equal to 2x 3x 2x sin 2x 2x sin 3x 3x sin 2x 3x sin 3x 2 sin x 3 sin x sin 22 32 sin 22 2x 2z sin 32 sin 2x sin 3x Which of the two expressions can be multiplied to obtain more expressions 3z sin 3x assume 0 Select all that apply E Part 2 of 3 2x sin 2x Select two or 2x sin 3x

Theo and Sasha start at the same place on a straight road riding bikes with the following velocities measured in mi hr Complete parts a through f VT 1 5 for 120 Vg t 10t for Osts2 and vg t 20 for 1 2 Theo Sasha Graph the velocity functions for both riders Choose the correct graph below JA 25 Av Q C OB Av 25 04 OC O D 25 Av

The cone and the cylinder below have equal surface area 3r O A True B False HY

Find the following lim cos 7a sin 0 0 cos 72 cos sin 72 sin cos 72 sin 7x sin cos 7x cos cos 72 sin sin 72 cos cos 72 sin sin 72 COS Consequently cos 72 sin 72 cos 7x cos 71 b sin 7x 8 Part 2 Part 3 o Part 4 of

CURRENT OBJECTIVE Use the washer method to find the volume of a solid of revolution around the x axis Question Let R represent the region bounded above by the graph of f x 4x 1 below by the graph of g x 2 and on each side by x 1 and x 4 What is the volume of the solid of revolution obtained by rotating R about the x axis Enter an exact value in terms of dow

6 Here is a graph of a pattern of numbers where V is a function of n The first point is 0 1 22 20 18 16 14 12 10 8 6 28 26 24 4 2 32 30 V 2 3 4 IMMathematics 5 a Plot the next 2 points on the graph that follow the pattern b Write an equation to describe the relationship between V and n f 1 1 f n f n 1 3 n 41 3 8

Question Let the curve C be the function f y 6y5 1 over the interval 1 y 7 Set up the integral for the arc length of the curve C Select the correct answer below 900y 1 dy T 1 30y dy 1 6y 2 dy 6y 1 1 dy of oy 1 dy GOLA 1 du

The velocity of an airplane flying into a headwind is given by v t 30 25 12 mi hr for Osts3 hr Assume that s 0 0 a Determine the position function for 0 t 3 b How far does the airplane travel in the first 2 hr c How far has the airplane traveled at the instant its velocity reaches 500 mi hr

The graph below is the function f x 8 7 6 5 4 3 2 8 7 6 S 4 lim 118 32 4 12 2 3 3 4 5 6 7 4 6 8 1 2 3 4 5 6 7 8 96 f x ter the limit If the limit is m enter go If the limit is enter oo If no limit exists

What is the surface area of the right cone below 15 8 A 304 units OB 184 units O C 496 units D 248 units

A cyclist rides down a long straight road at a velocity in m min given by v t 100 10t for 0 st 10 a How far does the cyclist travel in the first 4 min b How far does the cyclist travel in the first 8 min c How far has the cyclist traveled when his velocity is 75 m min

Given lim f x 2 and lim g x 1 evaluate 8118 X118 lim g x ln 6f x 4 60 8118 lim 69 x e f z 30 8118 lim 8118 lim 8118 6f x 49 a cos f x g x 11 2 1800 20 X X X X

Question Consider the curve f y y for 1 y 4 Find the arc length of the curv

Which of the following formulas would find the lateral area of a right cone where r is the radius and s is slant height A LA Trs B LA rs C LA rs D LA 2 rs

Given lim f x 7 and lim g x 4 evaluate 8118 lim 2f x 4g x 8118 lim 2 4f x 8118 lim x418 2f x 4g x 2 4f x 2 lim 2f x 4g x 2 4f x 8118 11

The surface area formula for a right cone is the same as the surface area formula for an oblique cone OA True B False

Question Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of f x xand g x 1 over the interval 1 3 around the x axis Hint graph the functions to determine which graph forms the upper bound and which graph forms the lower bound then use the washer method Provide your answer below

5 4 Quiz Which of the following formulas would find the surface where h is the height ris the radius LA is the lateral area and BA is the base area Check all that apply A P rh B 2 2rh C LA P D BA 2

Find the following values for f x sin Be sure your computing device is set to RADIAN mode X f x 0 8105 Based on these values O lim sin x 0 lim sin x 0 Olim sin x 0 0 0123 70 X 05 does not exist 0 X 0 5723 0 049453719922586 0 00191 X 0 6136 0 000127 X

Check all that apply sin 5x sin CT 5 5x 5x sin 6x 5x 6x sin 5x sin 6x 6 sin 5x 6x

Question 1 Consider the curve f x x for 1 x 2 Find the arc length of the curve 2x Provide your answer below

O is the center of the regular decagon below Find its area Round to the nearest tenth if necessary 14

Suppose 0 If u 2x then lim u x 0 lim 1 0 lim I 0 lim A 0 sin u u lim 0 sin u 1 u sin 2x x sin 2x 3x

3 A city bus charges 0 25 per ride if you first buy the 10 discount card Let B be the total cost in dollars of taking n rides on the bus a Complete the table for function B for several inputs h 71 10 0 10 2 95 4 8 5 B r b Sketch a graph of the total cost B in dollars for the number of bus rides from 0 to 10 2 c Write an equation for B as a function of n B 10 bus rides Cost less than 17 16 15 14 132129 10 2 4 6 8 10 B 0 10 Ben B n 1 25 n22

lim sin x 4 sin 4 T

Which of the following is the surface area of the right 2 OA 187 units OB 174 units G198 units

The graph of y f x solid and y g x dashed is shown AT 4 3 Find the following limits f x lim 2 4 g x 0 lim f x lim 2 4 g z 8 Does Not Exist 0 2 1 f x g z Does Not Exist 6 5 4 3 2 1 1 2 3 A 5 6 1 2 3 4 5 6

Given a right cylinder where h is the height and ris the radius what does the expression 2 th represent O A Area O B Lateral area O C Base area OD Volume

The lateral surface area of cone A is exactly the lateral surface area cylinder B A O A True OB False HT B

For this assignment please write a response to the following question Your response should be a minimum of 2 paragraphs and include at least 2 examples of positive incentives and 2 examples of negative incentives you avoid In general why do people approach positive incentives and avoid negative ones Why do people do this almost at the same time What are two things you like for incentives and two things you try to avoid

The two cones below are similar What is the height of the smaller cone O A 200 OB 5 28 5 O C 5 0 1 X 4 iffe

The two prisms below are similar What is the value of x O A 1 OB 10 O C 15 D 5 121 1 10 15

The ratio of surface areas of two similar solids is equal to the square of the ratio between their corresponding edge lengths OA True B False

The mayor of a town believes that over 47 of the residents favor annexation of a new bridge Is there sufficient evidence at the 0 01 level to support the mayor s claim State the null and alternative hypotheses for the above scenario Answer Ho Keyp Keyboard Short Tables

State whether the function is continuous at the given x values Justify your answers sqvt done lar 2x 1 x 1 7 f x 2 2 1 x 4 x 4 a x 3x at x 1 b at x 4 2 4 1 4 3 4 3 4

The graph of y f x solid and y g x dashed is shown 6 5 4 B Find the following limits f x lim 1 g x 818 0 Does Not Exist f x lim 2 1 g x 00 Does Not Exist 1 f z lim 2 1 g x 6 5 4 3 2 1 2 3 4 5 6 3 4 5 6

Find the limit sin 7x lim x0 sin 6x lim x 0 tan 6x sin 7x

5 Here are three patterns with their first 5 terms listed For each pattern de way to produce each new term from the previous term a Pattern A 5 8 11 14 17 FM 5 F 2 F n f n 1 3 nzz R b Pattern B 1 2 4 8 f 1 1 2 f n f n 1 nzl c Pattern C 0 1 3 6 10 f 2 12 f n f n 1 3 1 b 2

To find lim 2 0 cos x 1 which of the following steps might be useful 8 Multiplying numerator and denominator by Adding 1 to numerator and denominator Multiplying numerator and denominator by cos x 1

Solve the inequality and graph the solution Write the answer in interval notation 2c 123 or 3c 6 1111 111 6 5 4 3 2 1 0 1 2 3 4 5 6 0 2 U 2 00 6 5 4 3 2 1 2 U 2 00 0 1 31 6 5 4 3 2 1 0 1 2 U 2 00 2 3 4 5 6 E 2 3 4 5 6

Evaluate 3 2 3x lim 4x sin 2 0

Find the following lim cos 72 7x x 0 Question Help Written Example