Limits & Continuity Questions and Answers

Determine the Cartesian equation of the plane. F= (0,0,3) + S(1,1,4) + t(-2,1,5), (S, t) ∈ R

Use the graph to determine the limit. (If an answer does not exist, enter DNE.) (a) lim f(x)=_____ x->c+ (b) lim f(x)=_____ x->c- (c) lim f(x)=_____ x->c Is the function continuous at x = -3? (a) Yes (b) No

Solve the following system of equations using Cramer's Rule. 3x + 2y +z = - 4 4x-2y+z = 5 4x - 4y +z = 0 The solution is (Type integers or simplified fractions.)

Determine whether f(x) approaches ∞ or -∞ as x approaches 6 from the left and from the right. f(x) = sec(πx/4) lim sec(πx/4)=_____ x->6- lim sec(πx/4)=_____ x->6+

Consider the following function. f(x) =1/(x-5) Determine whether f(x) approaches ∞ or - as x approaches 5 from the left and from the right. (a) lim f(x)=_______ x->5- (b) lim f(x)=_______ x->5+

Consider the following function. f(x) =1/(x - 2)² Determine whether f(x) approaches ∞ or -∞ as x approaches 2 from the left and from the right. (a) lim f(x)=_______ x->2- (b) lim f(x)=_______ x->2+

Find the one-sided limit (if it exists). (If the limit does not exist, enter DNE.) lim (3 + 1/x) x⟶0-

Complete the table. (Round your answers to four decimal places. Assume x is in terms of radian.) lim 4cos(x)-4/x x→0 x -0.1 -0.01 -0.001 0 0.001 0.01 0.1 f(x) Use the result to estimate the limit. Use a graphing utility to graph the function to confirm your result. (Round your answer to four decimal places.) lim 4cos(x)-4/x = x→0

Consider the following function. f(x) =1/(x²-36) Complete the following table. (Round your answers to two decimal places.) x -6.5 -6.1 -6.01 -6.001 -6 -5.999 -5.99 -5.9 -5.5 f(x) ___ ____ ____ _____ ____ ______ ____ ____ ____ Use the table to determine whether f(x) approaches ∞ or -∞ as x approaches -6 from the left and from the right. lim f(x)=______ x->-6- lim f(x) =_____ x->-6+ Use a graphing utility to graph the function to confirm your answer.

Determine whether f(x) approaches ∞ or - ∞ as x approaches 2 from the left and from the right. f(x) = tan(πx/4) (a) lim f(x)=_______ x->2- (b) lim f(x)=_______ x->2+

Find the limit of the function (if it exists). (If an answer does not exist, enter DNE.) lim (x³ - 8)/(x - 2) x→2 Write a simpler function that agrees with the given function at all but one point. Use a graphing utility to confirm your result. g(x) = ____

What is the inverse of the following functions? f(x) = 6^x f(x) = 6^(x-1) f(x) = 1/2^x

The graph of the function f(x) = - 3 ˣ can be obtained from the graph of g(x) = 3ˣ by one of the following actions: (a) shifting the graph of g(x) to the right 3 units; (b) shifting the graph of g(x) to the left 3 units; (c) shifting the graph of g(x) upward 3 units; (d) shifting the graph of g(x) downward 3 units; (e) reflecting the graph of g(x) in the x-axis; (f) reflecting the graph of g(x) in the y-axis; Your answer is (input a, b, c, d, e, or f) Is the domain of the function f(x) still (-∞, ∞)? Your answer is (input Yes or No) The range of the function f(x) is (-∞, A), the value of A is

tan 8 =4/3 π < 0 < 3π/2. Find the exact value of b) cos 20 c) sin20 a) sin 20

In Exercises 11-18, use the point on the line and the slope of the line to find three additional points through which the line passes. (There are many correct answers.) om o Point 12. (3.-2) 14. (-4,1) 15. (0, -9) m = 0 m is undefined. m is undefined. m = -2

In Exercises 25-32, find the general form of the equation of the line that passes through the given point and has the indicated slope. Sketch the line by hand. Use a graphing utility to verify your sketch, if possible. Point Slope 26. (-3, 6) 28. (-2,-5) 29. (6, -1) m = -2 m = ³ m is undefined.

Let U= {1, 2, 3, 4, 5, 6, 7), A = {1, 4, 5, 7), and B = {1, 2, 4). Find the set (A U B)'.

A pair of dice is rolled. What is the probability of getting a sum of 5?

A survey of 100 people showed that 21 own a car, 68 own a bicycle, and 11 own both a car and a bicycle. How many people own a car or a bicycle?

Let D={16,19,21), List the elements in the set DUE. E = {16,18,19,20) and F = {15,17,18,19,21).

If the odds in favor of E occurring are 3:8, then find P(E) and P(E').

Determine the value of c such that the function is a probability mass function. f={(3,0.26),(4,0.34),(5,0.2).(6,c)}

Almost all companies utilize some type of year-end performance review for their employees. Human Resources (HR) at a university's Health Science Center provides guidelines for supervisors rating their subordinates. For example, raters are advised to examine their ratings for a tendency to be either too lenient or too harsh. According to HR, "if you have this tendency, consider using a normal distribution-10% of employees (rated) exemplary, 20% distinguished, 40% competent, 20% marginal, and 10% unacceptable. Suppose you are rating an employee's performance on a scale of 1 (lowest) to 100 (highest). Also, assume the ratings follow a normal distribution with a mean of 50 and a standard deviation of 14. Complete parts a and b. Click the icon to view the standard normal distribution table. a. What is the lowest rating you should give to an "exemplary" employee if you follow the university's HR guidelines? (Round to three decimal places as needed.) b. What is the lowest rating you should give to a "competent" employee if you follow the university's guidelines? (Round to three decimal places as needed.)

State whether the function is a probability mass function or not. If not, explain why not. p={(8,0.6), (9,0.8), (10,-0.4)} Select all that apply. A. p is not a probability mass function because it does not satisfy the third condition of probability mass functions. B. p is a probability mass function. C. p is not a probability mass function because it does not satisfy the second condition of probability mass functions. D. p is not a probability mass function because it does not satisfy the first condition of probability mass functions.

At a computer store, a customer is considering 9 different computers, 10 different monitors, 6 different printers and 3 different scanners. Assuming that each of the components is compatible with one another and that one of each is to be selected, determine the number of different computer systems possible.

A true-false test consists of 9 questions. a) In how many ways can the test be completed, selecting true or false for each question? b) What is the probability that a test is randomly answered perfectly?

A four-digit number starts with a number between 2-9 in the first position, with no restrictions on the remaining 3 digits. a) Find the probability that a randomly-chosen phone number contains all different digits. b) Find the probability that a randomly-chosen phone number contains at least one repeated digit.

Determine the total number of subsets of the set of letters from the English alphabet (a, b, c,..., k).

An election ballot asks voters to select five city commissioners from a group of twenty candidates. In how many ways can this be done?

The probabilities of events E, F, and EnF are given below. Find (a) P(EIF), (b) P(FIE), (c) P (EIF'), and (d) P (FIE) P(E) = 1/4, P(F) = 2/3. P(E∩F) =1/8 a. P(EIF) = (Type an integer or a simplfied fraction.) b. P(FIE) = (Type an integer or a simplfied fraction.) c. P (EIF) (Type an integer or a simplfied fraction.) d. P (FIE) = (Type an integer or a simplfied fraction.)

Assume A and B are independent events with P(A) = 0.5 and P(B) = 0.8. Find (a) P(A n B), (b) P(AUB). (c) P (A' B'), (d) P (A'n B), and (e) P (AMB'). (a) P(A n B)= (Type an integer or a decimal.) (b) P(AUB) = (Type an integer or a decimal.) (c) P (A'n B') = (Type an integer or a decimal.) (d) P (A' n B) = (Type an integer or a decimal.) (e) P (An B')=(Type an integer or a decimal.)

In a batch of 25 pedometers, 3 are believed to be defective. A quality-control engineer randomly selects 5 units to test. Let random variable X = the number of defective units that are among the 5 units tested. a. Find the probability mass function f(x) = P(X=x), and sketch its histogram. b. Find P(X= 1). What does this number represent? c. Find P(X≥ 1). What does this number represent?

Sample space S is partitioned into E₁ and E₂ such that P(E₁) = 0.30 and P(E₂) = 0.70. Let D be an event such that P(DIE₁) = 0.25 and P(DIE₂) = 0.45. a) Find P(D) and P(D') b) Find P(E₁ ID) and P(E₁ID'). c) Find P(E₂ID) and P(E₂ID'). a) P(D)= (Round to three decimal places as needed.) P(D')= (Round to three decimal places as needed.) b) P(E, ID) = (Round to three decimal places as needed.) P(E, ID') = (Round to three decimal places as needed.) c) P(E₂ ID)= (Round to three decimal places as needed.) (Round to three decimal places as needed.) P(E₂ID')=

a) Which pairs of events are independent? Select all that apply. One card is randomly chosen from a deck of 52 playing cards. Let G = the event that the card is a Jack, C = the event that the card is a Spade, and A = the event that the card is a Face Card (Jack, Queen, or King). a) Which pairs of events are independent? b) Which pairs of events are dependent? A. events G and A B. events G and C C. events C and A D. No pairs are independent. b) Which pairs of events are dependent? Select all that apply. B. events G and C C. events C and A D. No pairs are dependent.

Jeanine Baker makes floral arrangements. She has 11 different cut flowers and plans to use 7 of them. How many different selections of the 7 flowers are possible? How many ways can the 7 flowers be chosen?

You need to arrange nine of your favorite books along a small shelf. How many different ways can you arrange the books, assuming that the order of the books makes a difference to you? ways

In an experiment on social interaction, 4 people will sit in 4 seats in a row. In how many ways can this be done? There are ways.

An election ballot asks voters to select four city commissioners from a group of fourteen candidates. In how many ways can this be done? Four city commissioners can be selected from a group of fourteen candidates in _____ different ways.

A room contains 4 people, each of a different age. The people leave the room in random order, one at a time. What is the probability that they leave the room in ascending order of their ages (youngest to oldest)? The probability that they leave the room in ascending order of their ages is. (Round to six decimal places as needed.)

Find each coefficient described. 1) Coefficient of x² in expansion of (2 + x)⁵ 2) Coefficient of x in expansion of (x+3)⁵ 3) Coefficient of x³y² in expansion of (x-3y)⁵ 4) Coefficient of a²b² in expansion of (a-b)⁴

This boxplot shows the sales of water heaters over one year at Hefty Water and Heating. What is the median number of water heaters sold in 2014? F 18 G 20 H 28 J 34

Expand completely. 1) (2n+1)⁵ 2) (2m-1)⁴ 3) (v-2)³

Find an exponential regression curve for the data set x 0 1 2 y 9 25 80 An exponential regression curve for the data set is y= ___. e^_.x. (Type integers or decimals rounded to three decimal places as needed.)

Solve 2 sin² (w) + 3 sin(w) + 1 = 0 for all solutions 0 ≤ W< 2π W=

Without graphing the function y = 2 cos(- 8x), determine its amplitude and period. a)amplitude =___ b)period =___

Given u = 144i - 17j, what are the magnitude and direction of -3u? Round to the nearest whole number. 145; 97°

Simplify to an expression involving a single trigonometric function with no fractions. (cos(-x)/ (tan(-x) +( sin(-x)

Find a plane containing the point (-4,2,-2) and the line of intersection of the planes -5x + 6y-2z = - 86 and 7x + y - 4z= 18 ?

Vectors r, s, t, u, and v are shown on the graph. Which of the following vectors is equivalent to 2/3 v?

Indicate whether the graph specifies a function. The graph does specify a function. The graph does not specify a function.