Limits & Continuity Questions and Answers

7 Find the radius of convergence for a c R 1 R 2 00 k b d R 0 R 00

Let c a be nonzero real numbers such that c Find a given that 182 3 C 4 n 3 12 T rk e c a s f rdan farkl reel say lar ve c olsun E er 12 bulunuz ac c B O 70002 O 69660 O 70308 O 69984 69966 64152 n 3 182n 3 c 4 ac c F

2 Evaluate the limit lim 1 X 0

17 For each of the following scenarios write an inequality that compares the two quantities Neville has 8 in savings lain has 14 saved b Ray s account balance is 10 Mohamad s account balance is 13 C Jenny has made 74 selling ice creams Irene has made 119 selling lemonade d Uther has read 33 books this year His sister Patricia has read 12 books Tobias has 778 songs on his cell phone Marge has 525 songs on her tablet f Honolulu has a temperature of 98 F and Ottawa has a temperature of 38 F e a g The melting point of helium is 458 F The melting point of xenon is 169 F h Charlie has made 38 92 this week from his part time job Quiana has made 80 37 from her online craft store

4 5 pts Openstax 6 3 159 Use the method of cylindrical shells to develop the formula for the volume of a cone with radius rand height h Determine the equation of the line that defines the right edge of the cone

Answer each question below 22 What is the maximum number of turning points that the graph of m x 4x x 6x 9 can have 12 23 If cos cos 8 49 R and 0 8 then what does equal

If f x is a real valued function with the properties given as lim f x 3 x 2 then evaluate the limit lim I 2 OA The limit does not exist O Bl O c 3x 4 x 2 4 x O 013 and O EX6 lim f x 0 x 2

If f x is an increasing and negative valued function on the interval a b then which one of the following functions is also increasing on a b OA In f x 0 B 3 f x OC f x Darccot f x O E 1 f x 4

2 Find the limit at the indicated point if it exists a f x X 11 b f x 1 X 1 x 3x 10 X 2 x 2

Use the graph below to find the limits for questions 8 10 If the limit doesn t exist type DNE 5 4 3 2 1 lim f x lim f x 1 2 11 11 3 4 5

Question 10 Find Equation of Vertical Asymtotes g x 3x 2 x x 6 Ox 3 x 2 44 O none of these answers Ox 3 x 2

Oy 2x5 Question 20 finding the end behavior let f x 3x 4x 5x 1 hint for the f x given above infinity none of these answers O infinity Question 21 as x infinity f x as x goes to infinity f x goes to wh

Question 1 Find domain of this function y log x 2 O none of these O infinity infinity

Test the series for convergence or divergence Identify b 1 8 n 00 0 n 0 1 8n X Evaluate the following limit lim b 811 n Since lim b Ev 816 b for all n the series is convergent If the series is convergent use the Alternating Series Estimation Theorem to determine how many terms we need to add in order to find the sum with an error less than 0 000005 If the quantity terms 0 and b n 1 SV

How long will it take an investment to double in value if the interest rate is 8 compounded continuously Answer years

Construct a polynomial function with the following properties fifth degree 1 is a zero of multiplicity 3 2 is the only Answer her zero

Leave in reduced fraction form f x x 2 x 5 x 2 x 1 hole

5 10 points Consider the following graph given below 2 2 3 4 5 6 a On what intervals is f increasing b Find the interval s on which fis decreasing c On what interval s is f concave up d On what interval s is f concave down e What are the coordinates of the inflection points

A tank is filled with a fluid with density 73 The cross section of the end of the tank is given by the shaded region shown below that is bounded by the y axis the function written as y f z or z g y and the line y 15 as shown in the image below Note Assume c 6 m and d 15 m d The tank extends back a length of 10 meters as shown in the image below Our goal in this problem is to compute the work required to pump the liquid 3 meters over the top edge of the tank Basic Vars Funcs Trig Ay Report the volume force and work for a slice Note Type Delta x for Az or Delta y for Ay Delta must be capitalized Alternatively you can put your cursor in the box and when the CalcPad opens select Vars as shown below Y Volume of a slice xy f x or x g y Force for a slice y f x g y or X Work for a slice b kg m Az Length P Report the integral for the work Note a and b are the lower and upper limits of the integral

What is the range of the function y oot 3 x 8

Question 4 of 10 Step 1 of 1 Find the value of the following function at x 2 and x 3 Does the Intermediate Value Theorem guarantee that the function has a real zero between these two x values Answer f x x 2x 2x 7 f 2 f 3 Does the intermediate Value Theorem guarantee that there is a real zero between 2 and 3 Keyp Keyboard Shor

Solve the system by using any method If a system does not have one unique solution state whether the system is inconsistent or whether the equations ar dependent 5x y 10 x y 2 The system has one solution The solution set is O The system has no solution The system is inconsistent The equations are dependent O The system has infinitely many solutions The solution set is x is any real number The system is inconsistent The equations are dependent 0 0 X 010

11 3 of the sequence and are the first three terms of an arithmetic sequence what is the sum of the first 21 term 2 1375 5

Kuzey Sommer ame 1 For the following function give the vertical stretch period vertical and horizontal translation domain and range and sketch a graph y 2 tan x 3 3

Find the standard form of the equation of the parabola with the given characteristic s and vertex at the origin Directrix x 9

Dr3 5r2 1 9x6 4x 1 5x3 Hint Solve this problem the same way you would solve it to find the limit In order to have lim x 10 what number should we put in the

verse of following function it possible h x h x x 5 2 Answer How to enter your answer opens in new window Selecting a radio button will replace the entered answer value s with the radio button value If the radio button is not selected the entered answer is

Find the answer to the given limit and provide all the necessary justifications lim tan cos x tan e

Determine whether the series is convergent or divergent 6 sin 2 n 1 Step 1 The Limit Comparison Test allows us to determine convergence or divergence by considering lim n ob The terms Step 2 18 n a are positive since n is positive Since Now lim lim 718 If we substitute m 3 sin 2 then we have lim ce 0 then the terms sin 2 are positive sin 2 positi

Your task is to estimate how far an object traveled during the time interval 0 t 8 but you only have the following data about the velocity of the object Time seconds 0 Velocity feet per second 1 Q J To get an idea of what the velocity function might look like you pick up a black pen plot the data points and connect them by curves Your sketch looks something like the black curve in the graph below 3 1 2 3 1 1 Total distance Total displacement 4 5 6 7 8 4 1 4 3 2 7 8 You decide to use a left endpoint Riemann sum to estimate the total displacement So you pick up a blue pen and draw rectangles whose height is determined by the velocity measurement at the left endpoint of each one second interval By using the left endpoint Riemann sum as an approximation you are assuming that the actual velocity is approximately constant on each one second interval or equivalently that the actual acceleration is approximately zero on each one second interval and that the velocity and acceleration have discontinuous jumps every second This assumption is probably incorrect because it is likely that the velocity and acceleration change continuously over time However you decide to use this approximation anyway since it seems like a reasonable approximation to the actual velocity given the limited amount of data A Using the left endpoint Riemann sum find approximately how far the object traveled

For which r does the series 1 converge Remember to check endpoints if there is an interval of convergence n 0 In

1 Use one of the basic convergence tests to test for convergence kek k I

Use the Alternating Series Estimation Theorem or Taylor s Inequality to estimate the range of values of x for which the given approximation accurate to within the stated error Check your answer graphically Enter your answer using interval notation Round your answers to three decimal places cos x 1 0 843 0 843 24 lerror 0 00005

nd the 4th term in the sequence defined recursively 3 Qn 2an 1 5 lect one a 4 b 11 C 7 d 1

Does the following sequence converge or diverge 0 3 0 6 0 9 1 2 0 3n Select one O a It diverges O b It converges

the eighth term of the recursively defined sequence S and an an 1 8 for n 22 th term is

hat does the following sequence converge to 3n 5 3n converges to

hich of the following sequences is divergent elect one a Ob C O d O e 100n 1 Vn n 200 n

Use Maclaurin series to find What is the radius of convergence sin x I

Find the largest value of log5 x log5 x 4 that satisfies 6

Find all zeros of the function f x 3x 30x 93 90 Enter the zeros separated by commas Queri T

17 Find all horizontal and vertical asymptotes of f x 626 22 102 52 3 nos

12 lim f x 1 81x lim f x 2 2 lim f x 1 8178 f 2 1 2 0 lim f x x 24 26 lim f x 2 2 2 lim f a x 2 0

20 If f x 2 1 2 2 1 if a 1 if a 1 find lim f a if it exists Is lim f x f 1 if a 1

Use the given information Center 11 8 Radius 4 to write the equation of the circle O x 11 y 8 16 O x 11 y 8 16 O x 11 y 8 4 O x 11 y 8 16

Let p x be the density function given by Find the mean value of p x p x 276 2 11 0 if 0 x 12 2 253 if 12 x 23 otherwise

estion 3 Determine a and b in such a way that the given function f x is continuous at x 3 Type your solution co f x if x 3 3a if x 3 x 2ax 3x b 6a if x 3 D

Determine a and b in such a way that the given function f x is continuous at x 1 f x a sin x 1 if x 1 b 1 if x 1 bx b x 1 if x 1

9 6 Start from the given graphs and sketch the graph of the function g State the domain range and asymptote if any g x ln x 3 y In x Domain Range Asymptote

stion 1 Find intervals of continuity of the given function and explain and justify your answer f x x cos x tan x 4