Limits & Continuity Questions and Answers

Refer to the function f shown to the right Use the graph to estimate the indicated function values and limits Complete parts A through E below A lim f x x 3 Select the correct choice below and if necessary fill in the answer box to complete your choice O A lim f x Type an integer x 3 ACCED

Let f x sec x a Find f x recommended b Check to see that your answer to part a is reasonable by graphing f and f for lx 2 30 R 2 Describe the relationship between the two graphs O Note that f 0 where f has a minimum Also note that f is negative when fis decreasing and f is positive when fis increasing O Note that f 0 where f has a minimum Also note that f is positive when fis decreasing and f is negative when f is increasing Note that f 0 where f has a minimum Also note that f is decreasing when fis negative and f is increasing when fis positive O Note that f 0 where f has a maximum Also note that f is negative when fis decreasing and f is positive when fis increasing 2 00

1 1 x a Find an equation of the tangent line to this curve at the point nt 1 The curve y y b Illustrate part a by graphing the curve and the tangent line on the same screen y 2 0 1 5 4 C 4 is called a witch of Maria Agnesi 2 2 1 8 0 5 0 5 1 0 y 2 0 1 5 0 5 0 5 1 0 2 2 4 4 X 4 2 y 2 0 1 5 1 9 0 5 0 5 1 0 2 4 2 y 2 0 S 1 0 0 5 0 5 1 0 2

Two adjacent sides of a parallelogram are 3473 and 4822 respectively The angle between these two sides is 72 23 Find the length of the longer diagonal 4822 Dr 3473 b a 72 23 A C B Round to the nearest foot

Given this unit circle what is the value of x X x 1 10 1 0 Enter

Use the graph of y f x 7 y f x to graph the given function 3 of

x 9 Consider the graph of the function f x x 2x 15x What are the vertical asymptotes Just list the x values separated by commas Provide your answer below

Find all the intercepts either x or y of the function Provide your answer below x 9x x 3 Enter ordered pairs in the form x y

4 Find the amount of each payment to be made into a sinking fund earning 5 compounded monthly to accumulate 95 000 over 4 years Payments are made at the end of each period The payment size is Do not round until the final answer Then round to the nearest cent

dentify the rational function whose graph is given below Note that the function has an x intercepta tercept at y 7 6 5 4 15 10 5 10 15 1 2 3 4 5 6 7

Find the payment necessary to amortize a 12 loan of 1300 compounded quarterly with 16 quarterly payments The payment size is Round to the nearest cent

Find the monthly house payments necessary to amortize a 6 0 loan of 258 600 over 30 years The payment size is Round to the nearest cent www

2 Find the payment necessary to amortize a 12 loan of 1300 compounded quarterly with 16 quarterly payments The payment size is Round to the nearest cent

4 Find the monthly house payments necessary to amortize a 10 8 loan of 166 100 over 25 yea The payment size is Round to the nearest cent

Find the pivot in the simplex table Do not solve X1 4 6 16 X2 S1 2 z 6 4 1 0 0 24 0 1 0 42 12 0 0 1 0 O4 in R2 and C2 O 6 in R2 and C1 O4 in R1 and C1 O6 in R1 and C2

Graph by setting the moving points correctly Provide your answer below 10 3 0 10 5 4 0 f x 5 x 1 x 3 6 5 0 10

Select all correct answers Select all that apply As x3 f x As x 3 f x As x 3 f x 3 t 14 0 1 0 2 1 8 Asx3 f x 21 Fin

lim 318 n 1 n n6 8 n n n n 8 O converges O diverges lim 818 11 11 Points DETAILS LARCALCET7 9 4 025 MI Use the Limit Comparison Test to determine the convergence or divergence of the series 00 L 0 nk 7 k 2 L 0

erges O diverges Submit Answer 5 56 11 11 Points DETAILS lim 818 Use the Limit Comparison Test to determine the convergence or divergence of the series 8 3 3 n 0 n 3 1 1 3 6 72 PREVIOUS ANSWERS LARCALCET7 9 4 019 L 0

Find the horizontal asymptote for the function given below Give your answer in the form y b or enter if there is none 7x 3x 1 3x4 5x 2 f x

Use power series to solve the initial value problem x 2 y 8xy 6y 0 y M8 x n n 0 y 0 1 y 0 0 n 1 help formulas

Find the limit lim X X 4x 2 7x 4

Use the given graph of f x x to find a number such that if x4 8 then x 2 0 4 8 9 YA 2 4 2 1 6 0 4 y x x

Suppose that the polynomial function f is defined as follows f x 9 x 6 x 5 x 7 List each zero of faccording to its multiplicity in the categories below If there is more than one answer for a multiplicity separate them with commas If there is no answer click on None Zero s of multiplicity one Zero s of multiplicity two Zero s of multiplicity three 0 0 0 0 0 None S

Find the limit lim X 6x 4 4x 7

Explain why the function is discontinuous at the given number a Select all that apply f x lim X 3 1 x 3 lim f x does not exist X 3 f x and lim x 3 f x are not finite and are not equal f 3 is undefined f 3 and lim f x are finite but are not equal X 3 Onone of the above Sketch the graph of the function y 4 X

Use the graph of the function y 10 8 6 2 4 6 8 10 3x given below to estimate the open intervals on which the function is increasing or decreasing 10 X

Evaluate the definite integral S 10x 7 dz Liitt THE I 1

For the parabola graphed below state the x values where the function is increasing and where the function is decreasing Give your answers an inequalities 10 9 7 8 7 6 5 4 3 2 10 9 8 7 6 5 4 3 2 1 2 3 4 5 S676 a 6 7 8 9 10 1 2 3 4 5 6 7 8 9 IC The graph is increasing when 3 x 00 The graph is decreasing when x 3 q X x invalid inequality notation

Solve the equation and enter its solution set If there is no solution enter no solution in the blank 4a 1 8 3 Type your answer and submit X X 22 6 Hint I You are incor

Question 8 Evaluate the limit lim H18 5 9x 6 2x Question Help Video Messa

A rock weighing 32 0 g is placed in a graduated cylinder displacing the volume from 12 3 mL to 16 8 mL What is density of the rock in g cm density g cm I Record your answer to the tenths place Density g cm Enter

Simplify sin x cos x cos x sin x

Write the sum using sigma notation A 1 2 3 4 138 B where A B n 1 Question Help Video Message instructor Calculator

Find the magnitude of the resultant vector 8 10 1 W 7 1 Round to the nearest tenth Ente

Dalton plays on his high school s baseball team and his friend Caleb plays on the high school s lacrosse team Since both teams have several of the school s most prolific scholars they wondered which team has a greater cumulative GPA on average They randomly selected 20 baseball players and 20 lacrosse players and found each player s cumulative GPA with the help of a guidance counselor The results of the survey are shown in the accompanying samples A player on each team has a 3 92 cumulative GPA Use Excel to calculate the z score for the data value that represents the player with the 3 92 GPA for each team Round your answers to two decimal places Provide your answer below Thez score for the player of Baseball 3 76 3 92 2 69 3 56 3 36 2 95 2 57 3 75 3 3 Lacrosse 3 02 Help Copy to Clipboard 2 92 3 93 2 98 2 83 3 1 3 9 2 72 3 86 Download CSV

Graph on the number line the set of all real numbers between 5 and 5 including 5 and excluding 5 and express in interval notation O A O C 6 6 5 O A 5 5 OB 5 5 OC 5 5 OD 5 5 5 4 4 3 2 3 2 1 1 0 0 1 2 3 2 3 4 4 5 5 COL 6 6 O B O D 6 6 L 5 5 4 4 3 3 Which of the following represents the set of all real numbers between 5 and 5 including 5 and excluding 5 expressed in interval notation 2 2 0 10 1 1 2 2 3 3 4

q066P Lion f is represented in the table te f 3 X f x 74 0 1 2 3 5753 23 4 5 6 28 3 7 10 3 7 33 7 45 6 8 3 47

Assume that a population P of wolves in a region is proportional to the area A of the region Does it make sense to use differential equations to model the population size If so write the differential equation If not explain why A

What is the amplitude of the following equation y sin x 2 T Enter

What is the period of the following function y cos 50 T

2 lim 6 Find the limit x 0 sin x

Sketch a graph of the function f x cos x T 4 TL 4 Clear All Draw M TL 2 37 4 R 57 4 3 2 7 4 27

Find the horizontal and vertical components of this vector 10 f 17 Round your answer to the nearest tenth Enter

Given the triangle 30 x 31 17 answer to 4 decimal places find the length of side x using the Law of Sines Round your final a

Evaluate the following limits If needed enter oo for oo and oo for oo You can use a tool like desmos com to create a graph to help with part a lim 818 x 3x 1 1 x

7 For what values of x does the following power series converge n x 3 n 1

Let f x lim 43 8 x x 2x 3 Calculate the following limits Enter DNE if the limit does not exist f x lim 43 f x if x 3 if x 3 lim f x 3

Given that a lim lim f x 0 x18 lim g x 0 x a lim h x 1 X 8 lim p x co x18 evaluate if the following limits are not indeterminate forms If a limit is indeterminate enter INDETERMINATE c lim lim g x 0 X 8 x a g x b lim f x x a p x h x x a p x d lim P x x a q x

Sketch a possible graph of a function that satisfies the conditions below Determine whether f is continuous at x 2 f 2 2 lim f x 2 lim f x 2 X 2 X 2 Choose the correct graph below A Ay OU Is f x continuous at x 2 OB Ay CIB O C AY ON O D