Limits & Continuity Questions and Answers

5 3 13 a cos b sec soc 5 3 in 77 3 c sin

37 40 Reference Numbers Find the reference number for each value of t 37 a t c t 4T 3 7TT 6 turibau b t 5T 3 d t 3 5

unit circle 3 mlin 3 5 4 5 lis

A function is given below Evaluate the indicated limits numerically Enter INF for INF for or DNE if the limit does not exist but is neither o nor Don t forget to check for common factors If you forget how to factor a cubic try an online calculator a lim f x x 5 b lim f x x 5 c lim f x x 5 f x x 4x 3 x3 8x2 5 50 help numbers

K Solve the equation 3x 8 6x 3x 1 Select the correct choice OA There is one sol

and Question 7 Solve the equation Be sure to chec 6y 4 9y 11 Select the correct choice below an

Problem 2 15 points Evaluate 3 sin x lim In x 0 X Show each limit law applied answers that do not do this will receive NO

per r Equations K Solve the following 4x 28

Write the equation of the trigonometric graph Use a positive coefficient on sine for this activity jr y sin 2 try 1629 T T 39 ajn

Which of the following shows the extraneous solution to the logarithmic equation below log3 18x log3 2x log3144 O x 16 Ox 8 Ox 4 Ox 2

What is the solution to the equation below log 4x log x 2 7 2 12 0 X orx 3 10 X 10x 3 9

Complete the table y f g x sin sin 5 U u g x y f u y sin u

3 f x x x 1 x 2 You must complete ALL four parts if choose 3 a Determine end behavior of f x Explain reasons Don t use a calculator b Find the zeros of f x State whether the graph crosses the x axis or touches the x axis and turns around at each intercept c Find the y intercept Door the graph has y axis symmetry origin symmetry or neither

12 0 52 Points DETAILS 8 LARCALC12 2 3 073 Find an equation of the tangent line to the graph at the giv y 8 4 f x 16 x x 16 4

Given the function g x x 6x 12 determine the average rate of change over the interval 1 6

X27 f x 58 f x 46 g x 1 7 f x If h x f x g x j x and k x g x f x g x then use the chart above to answer the following Find the value of each of the following ANSWER IN FRACTION FORM h 2 j 2 k 2 h 7 j 7 k 7 g x 8 8

2x 1 x 7 Find the slope and the equation of the line tangent to f x The slope of the line tangent to f x at x 2 is Answer the following in slope intercept form y mx b The equation of the tangent line is y at x 2

How many songs can a digital music player hold The data below represent the memory x and the number of songs n Complete parts a through f below Memory x Number of Songs gigabytes 8 16 32 n 2050 4100 8200 16400 LEX a Plot the ordered pairs x n in a Cartesian plane Choose the correct graph on the right b Show that the number of songs n is a linear function of the memory x A linear function has a constant average rate of change The average rate of change between 4 2050 and 8 4100 is

The second proposal we ll consider is a modified flat tax plan where everyone only pays taxes on any income over 20 000 So everyone in group A will pay no taxes Everyone in group B will pay taxes only on 9 000 1 Determine the total taxable income for the whole population Show your work 2 Determine what flat tax rate would be necessary to collect enough money in this modified system Remember the government needs 800 000 Show work 3 What are the pros and cons for this plan 4 Complete this table with the data for both the plans I will include a Word document on D2L with all of the following tables to help you with this part You should be able to copy and paste into your project document

Suppose that the functions fand g are defined as follows Find f x x x 9 g Simplify your answers Then give its domain using an interval or union of intervals 2 0 g Domain of g x 1 0 g 4 x 3 O 0 0 0 0 0 8

Graph the following function using the techniques of shifting compressing stretching and or reflecting Start with the graph of the basic function y x and show all stages Be sure to identify at least three key points Find the domain and the range of the function f x x 3 5 Use the graphing tool to graph the equation Click to enlarge graph Fill in the missing coordinates of the points that lie on the graph of y x and the corresponding points that lie on the graph of f x x 3 5 Points that lie on the graph of y x Simplify your answers 1 0 1 Corresponding points that lie on the graph of f x x 3 5 Type ordered pairs Simplify your answer The domain of f x is Type your answer in interval notation The range of f x is Type your answer in interval notation

Find the real solutions of the equ 9x 7 7

Find the missing numerator that will make the rational expressions equivalent y 3 5y2 8y 4 5y 2 y 2 3y 2

a Use a graphing utility to graph f x maxima and local minima

Use the graph of the function f given below to questions

suppose that t is irrational number then show that at least one of t 2 or t 3 is irrational

3 The graph of a sinusoidal function with two labeled points is given below 4 points 1 18 a Determine the equation of the midline m 6 2 b Determine the amplitude c Determine the period of the function then determine the value of B for a function written in the form y A cos B x C D Assume B is positive d Write the function as a transformation of y cos x Provide justification for any horizontal shifts e Write the function as a transformation of y cos x Provide justification for any horizontal shifts

Expenses FICA State Income Tax Federal Income Tax Medical Insurance Amount Taxed n 4 900 00 7 400 00 2 000 00 A 14 300 B 79 300 C 51 700 700 What is the net take home pay for an individual with expenses shown who has a gross income of 65 000

1 Guess the value of the limit if it exists by evaluating the function at the given numbers correct to six decimal places f x frac x 2 3 x x 2 9 a b lim f x x 3 lim f x x y c Use part a and part b to guess lim f x x 0

1 Given function 2 f x y In 2 x 1 x y do the following 20 points 8 and 12 a Find and sketeh the domain of f b Does f x y lim x y 1 0 exist Why or why not

fn 2 Prove that lim n where as 0 n 1 1 x nx 0 Lo fala S fn x dx when 0 x 1 when x 1 1 2 lim fn x dx 0 n

Solve the linear inequality Express the solution using interval notation 5 4x 72x Graph the solution set Use the tools to enter your answer 10 6 2 2 co 6 8 10

4 a A tank contains 5000 L of pure water Brine that con tains 30 g of salt per liter of water is pumped into the tank at a rate of 25 L min Show that the concentration of salt after t minutes in grams per liter is C t 30t 200 t b What happens to the concentration as to

A pair of dice is rolled Find the probability of rolling a a sum not more than 7 b a sum not less than 7 c a sum between 4 and 9 exclusive 21 Simplify your answer 7 The probability of rolling a sum not more than 7 is 12 Type an integer or a simplified fraction b How many ways can two dice be rolled such that their sum is not less than 7 21 Simplify your answer 7 The probability of rolling a sum not less than 7 is 12 Type an integer or a simplified fraction c How many ways can two dice be rolled such that their sum is between 4 and 9 exclusive

Which set of ordered pairs has a range of 0 1 4 O 0 0 0 1 4 1 O 0 2 1 2 4 2 O 0 0 0 1 0 2 0 4 O 1 0 0 1 2 1 3 4

Sketch the graph of the function Include two full periods y cos 5 3 2 1 R 1 2 3 4 5 W N y 2 1 5 0 5 4 8 0 5 1 1 5 2x O 8A 4 2 2x X 2x O 2 X R 4 3 2 1 1 y 2 1 5 0 5 0 5 1 1 5 2 A x 4 27 x

Find the period and amplitude y 5 sin sin TX 5 period amplitude

2 For each of the following functions determine the points at which the function is discontinuous and state the type of discontinuity removable jump or infinite a b d c 3x 4 43x x k x X Ir x 1 5x 6 T 3 31 x 2 3 x x 4 3x 6x 3 2 20 if x 1 if 1 x 1 if x 1

Evaluate the limit 2 81 x 9 If the limit does not exist enter DNE lim

A rectangular garden is 5 ft longer than it is wide Its area is 414 ft2 What are its dimensions ft width length ft

Evaluate the definite integral 30V f 3x x 4 dx

1 point Let g x f t dt where f t is given in the figure below Find each of the following A g 2 Click on the graph for a larger versi 1 0 K 2 1 0 B g 3 C The interval with endpoints given to the nearest 0 25 where g is concave up interval Give your answer as an interval or a list of intervals e g infinity 8 or 1 5 7 10 or enter none for no intervals D The value of a where g takes its maximum on the interval 0 8 to

Divide the polynomial P x x 3 5x 2 3x by x 1 using synthetic division

MTH 201 Homework 6 Find the exact numerical value of each expression

7 Sketch the following graph of an example of a function f that satisfies all of the following conditions a lim f x 2 24 4 b lim f x 1 1 c lim f x 1 24 1 d limf x e limf x DNE 1 3 f lim f x 0 1 3 5 4 3 2 7 5 4 3 2 1 0 1 2 3 4 2 3

be the following piecewise defined function f x left begin array II x 2 3 text for x leq 5 5 x 3 text for x 5 end array right a Is f continuous at X b Is f differentiable at x 5 a Is 5 f x continuous at x 5 2 Yog No

4 Find each limit or explain why it doesn t exist a lim 3 b lim f x DNE BECAUSE 9 5 comes from 10TT while right c limf x 2 0 Being to d lim f x 214 1 e limf r DNE f lim f x 84x 20 g limf r 3 2 1 3 2 1 0 1 2 4 5

2 lim In cos r l m loccosx In X 27

Given f x 5 x 6 4 classify each statement about as true or false The point of symmetry on f x is 4 6 The domain of f x is 4 The graphs of f x and f x are reflections across the x axis The range of f x is True O O O O False O O

The graph of a function y f x is shown below Use it to answer the following questions Enter DNE if a value does not exist enter o if the limit approaches positive infinity or the limit approaches negative infinity YA 4 3 2 1 Aluf 4 3 2 1 2 3 4 5 6 1 2 5 20 What is a reasonable estimate for lim f x 2 3 What is a reasonable estimate for lim f x What is the best description of the function at x 3 Select an answer O What is a reasonable estimate for lim f x x 6 What is a reasonable estimate for lim f x 2 6 What is a reasonable estimate for lim f x x 6 What is the best description of the function at x 6 Select an answer X