Limits & Continuity Questions and Answers

Sketch the graph of the function by applying the Leading Coefficient Test finding the real zeros of the polynomial plotting sufficient solution points and drawing a continuous curve through the point f x x 16 a Apply the Leading Coefficient Test The graph of the function rises to the left and rises to the right The graph of the function rises to the left and falls to the right The graph of the function falls to the left and rises to the right The graph of the function falls to the left and falls to the right b Find the real zeros of the polynomial Enter your answers as a comma separated list If there is no solution enter NO SOLUTION c Plot sufficient solution points P X x 2 1 0 1 2 4

Graph the solution set of the inequality where x is X 12 Unte

Use a vertical shift to grap y cosx 6

Figure 10 P2 3 Pl Price A OD B C D A B Q2 B D D Refer to Figure 10 Total revenue when the price is P is represented by the area s Q1 Demand Quantity

Find the domain of the following vector valued function r t t 10i t 1j Select the correct choice below and fill in any answer box es to complete your choice OA t sts OB tts OC t tsortz OD ttz

t K Let statements p q r and s be as follow p ZA and ZB are a linear pair q ZA and ZB are supplementary r ZA and ZB are adjacent angles s ZA and ZB are adjacent and s and write the

Select True or False for each statement You must get all of the answers correct to re credit True In a 5c 5c In a In b ln b 4 In x a ln x In 23 In 25 In 22

K Write the converse inverse and contrapo If I am in Seattle then I am in the We

29 tan 38 cot 68 What is the first step to find e A 60 30 180 OB 68 38 90 O C C 30 60 90 D 30 60 180

33 Draw and label a right triangle using the given sides then solve for the unknown side and write the trigonometric functions of angles A and B if a 5 and c 7 side b OA 2 6 OB 2 O C 12 D 74

41 44 Use the Intermediate Value Theorem to show that there is a solution of the given equation in the specified interval 42 x 1 x 0 1 41 x x3 0 1 2 43 e 32x 0 1 44 sin x x x 1 2

se the following summary of notation used for simple and compound interest to answer the PV principal or present value FV future or maturity value Tannual stated or nominal interest rate t number of years m number of compounding periods per year interest rate per period i n total number of compounding periods E effective rate APY What is the difference between r and i he annual interest rate r is only equal to the interest rate per period i if interest is compoun therwise i

Your itinerary contains a grid map of Washington D C with each unit on the grid representing 0 125 miles If Arlington Cemetery is located at 6 2 and the Pentagon is located at 13 4 what is the direct distance not walking distance which would have to account for bridges and roadways between the two landmarks in miles Round your answer to two decimal places if necessary Answer 2 Points

Find a formula for the inverse of the function f x f x 5 9x

A Find a formula for the inverse of the function f x 2 3 5 f x 3 5 x x 0

35 y 1 2 x 5 y 3x 20 In the xy plane a point with coordinates h k lies in the solution set of the system of inequalities above What is the maximum possible value of h

Enter a Y for Yes or an N for No in each answer space below to indicate whether the corresponding function is one to one or not You must get all of the answers correct to receive credit 1 k x x 6 5 x 7 2 f t tant t 3 k t 4 t 6 4 f x sinx 0 x 5 g t 5t 5 6 h x x 3

Prove that a sequence Xn neN of vectors in Rd converges if and only if each one of th sequences n 1 neN En 2 nEN Ind neN converges

A 2 4 8 10 16 rt or to make the given statement true 0 A THE ose the correct answer below that makes a true statement 2 4 8 10 16

IS raph the equation using the x and y interce x y 2

point nd the limits sin 3t i lim t 0 sin 2t lim t 3 t 27 3 i In sin 3t j tln 3t k In tan 2t t 5t 6 t t 6 Oj 3 2i Ok j 3 t 3 ln t 3 k 27i 3j 0k

14 15 Use the definition of continuity and the properties of lim its to show that the function is continuous at the given number a 14 f x 3x4 5x 3 x 4 a 2 15 f x x 2x 4 a 1

Find the values of x between 0 and where the tangent line to the graph of y sin x cos x is horizontal Use symbolic notation and fractions where needed Give your answer as a comma separated list of x coordinates X

Given that f x x h x h 1 4 h 1 7 Calculate f 1 27 Hint Use the product rul

For the following demand equation compute the elasticity of demand and determine whether the demand is elastic unitary or inelastic at the indicated p x 29 p 8 E 8 the demand is Select

2 Evaluate lim t 0 176 i sin t t 1 j tan t 1 t

The amount of copper ore produced from a copper mine in Arizona is modeled by the function f x 100 36x where x is the number of years since 2005 and f x is measured in thousands of tons a Sketch a graph of f 900 800 700 600 500 400 300 200 100 900 800 700 600 500 10 15 20 25 30 X 900 800 700 600 500 400 300 200 100 900 800 700 600 f 500 5 10 15 20 25 30

Let f x 5x 11x 2 Using the definition of derivative f x lim h 0 enter the expression needed to find the derivative function f x lim h 0 f x h f x h df After evaluating this limit we see that f x dx Finall

15 a tan 5 T 6 o bi sa entendi gibi 5 T b cot 6

1 a What is the unit circle and what is the equation of the unit circle b Use a diagram to explain what is meant by the terminal point P x y determined by t 47 4 1 7 2 0 1 d What is the reference number associated with t 2 e Find the reference number and terminal point for T t 2 2 17 7 1 8 6 57 2 dese 4 TT c Find the terminal point for t 2 2 Lett be a real number and let P x y be the terminal point determined by t a Write equations that define sin t cos t tan t csc t sec t and cot t b In each of the four quadrants identify the trigonometric functions that are positive c List the special values of sine cosine and tangent 3 a Describe the steps we use to find the value of a trigono metric function at a real number t 5 T 6 b Find sin c Find sin 4 a What is a periodic function b What are the periods of the six trigonometric functions nolisnu 19T 4 2 2 5 a What is an even function and what is an odd function b Which trigonometric functions are even Which are odd c If sin t 0 4 find sin 1 d If cos s 0 7 find cos s

ssignment when you send the proje nd I D number at the top of this pag his project will count for 5 of your nd assemble all the necessary mat complete it on paper Feel free to at When you have completed this proj anagement system by scanning th Microsoft Word document format ocument in gif image format Usin

esearchers measured the average blood alcohol concentration C t of eight men starting one hour after consumption of 30 mL of ethanol corresponding to two alcoholic drin Round your answers to two decimal places t hours 1 0 1 5 2 0 2 5 3 0 C t mg mL 0 35 0 25 0 19 0 13 0 09 a Find the average change of C with respect to t over each time interval i 1 0 2 0 ii iii 1 5 2 0 2 0 2 5 iv 2 0 3 0 b Estimate the instantaneous rate of change at t 2

Select all of the following statements which are true If A and B are invertible then AB A B DIf a matrix is invertible then it s inverse is unique Every identity matrix is invertible All square matrices are invertible

Find the limits a lim f x X 7 f x x 6 g x x b lim g x X 8 c lim g f x X 7

Find the period y 3 tan x Graph the function O 2 PAX O 12

The trigonometric function y tan x has period 32 2nx n is an integer x nx n is an integer Ox 2nx n is an integer 0x 1 2 2 x 2nx n is an integer x 1 2 nz nx n is an integer Sketch a graph of this function on the interval 1 2 1 2 1111 10 and the following asymptotes L HIN 10

QUESTION 1 Fill in the blanks in each of the following equations Question 452 is another way of saying 172 49

For questions 3 6 refer to the graph of k x below 3 a Does k x have an absolute minimum O Yes O No b Explain using complete sentences and or appropriate mathematical symbols and terminology your answer from part a y k x y 1 5 4 3 2 1 3 5 4 Estimate all x y coordinates where k x has a local maximum Answer 2 Answer 10 5 On which interval s of the domain is k x decreasing Place your answer in the box below

The time taken to create a specific 3D printed product can be described by the probability density function f t 0 5t 0 t 2 minutes a Show that f t is a valid probability density function b What is the probability that a 3D printed part takes less than 1 minute to create c Calculate the median time taken to print a 3D printed part HINT 50 of the time it will be quicker than the median to make a 3D printed part and 50 of the time it will take longer than the median

x t as shown in figure 5 a Write the mathematical function for x t using step and ramp function b Plot 2x 0 5t 2 2

Write the domain in interval notation a y t 9 t b w t 1 9 c z t 1 9 t Part 1 of 3 a y t 9 t The domain in interval notation is 0 0 Part 2 of 3 K OVO 0 0 0 0 0 0 8 X

Assignment 3 Proble Previous Problem Problem List Next Pr 1 point Let f x 1 3 x 1 lim f x x 4 4x 18 if x 4 if x 4 if x 4 Calculate the following limits Enter DNE if the li

for x 4 for x 4 5x c In order to make f x continuous on what number should c be equal to 8 1 point Suppose f x C If there is no possible value of c that makes f x continuous for all real x enter none Preview My Answers Submit Answers

Radian Measure Degree Measure Sin Cos Tan Cot Sec Csc 3r 2 540 7 3 150 13 4 210 7 T 4 270

State if the given angles are coterminal 11 185 545 Find a coterminal angle between 0 and 360 13 330 15 640 17 19 11 Find a coterminal angle between 0 and 2x for each given angle 35t 18 3 12 15T 4 14 435 17x 161x 36 36 16 442 18 20 19t 12

stat A f 1 FFFERS B lim f x x 1 3 b Evaluate each of the following values If the value does not exist write 5 C lim f x x 1 D lim f x x 1 c Is f x continuous at x 1 If so then show this fact if not then e use limits to support your answer

limit doesn t a lim f x 3 x 0 b lim g x 4 2 c lim f x g x x 2 a 3 3f x 2 1 y 6 4 12 3 3 5 g x f x e Is f x continuous If not where is it not continuous and why X 6 anything Stonning

Evaluate the following limits if they exist If not answer D N E or 0 You are expected to use the techniques taught in this chapter Show work L Hospital s Rule is 3 not allowed because we haven t learned it yet 8 lim x 4x x 10x 25 10 points each

2 Find gof x given that f x x 1 and g x x 2 8 points

Use the table feature of your calculator and the Location Principle to find the zeros of x 4 5x 3 x 2 10x 2 0 to the nearest hundredth