S x y

As an example of applying the third condition in Definition 5.2.1, the joint cd f for continuous random variables X and Y is obtained by integrating the joint density function over a set A of the form. A = {(x, y) ∈ R2 | X ≤ a and Y ≤ b}, where a and b are constants. Specifically, if A is given as above, then the joint cdf of X and Y, at ...

Mar 24, 2023 · This pattern works with functions of more than two variables as well, as we see later in this section. Example 14.5.1: Using the Chain Rule. Calculate dz / dt for each of the following functions: z = f(x, y) = 4x2 + 3y2, x = x(t) = sint, y = y(t) = cost. z = f(x, y) = √x2 − y2, x = x(t) = e2t, y = y(t) = e − t. The Choose-an-Element Method. The method of proof we will use in this section can be called the choose-an-element method.This method was introduced in Preview Activity \(\PageIndex{1}\).Bếp điện từ hiện đại có thể đem lại hiệu suất đun nấu cao và tiết kiệm chi phí đáng kể cho bà nội trợ, tuy nhiên việc bảo quản thiết bị điện cần được duy trì ...X&Y is the third studio album by British rock band Coldplay. It was released on 6 June 2005 by Parlophone in the United Kingdom, and a day later by Capitol Records in the United States. The album was produced by Coldplay and producer Danton Supple. It is noted for its troubled and urgent development, as well as manager and creative director ...Split the string into two non-empty substrings at a random index, i.e., if the string is s, divide it to x and y where s = x + y. Randomly decide to swap the two substrings or to keep them in the same order. i.e., after this step, s may become s = x + y or s = y + x. Apply step 1 recursively on each of the two substrings x and y.

Máy cán bột SXY-35 (TMTP-LB18) chuyên dùng trong quá trình sản xuất các loại bánh bao, bánh gối, bánh pizza và cả những loại bánh nhiều tầng liên hệ hotline ...In fact |x − y|2 = (x − y)2 | x − y | 2 = ( x − y) 2, so nothing to gain from that. If you're familiar with the triangle inequality, this actually is the triangle inequality for x x and −y − y, since | − y| =|y| | − y | = | y |. – Matt Samuel. Dec 18, 2018 at 4:26. so does it follow to say |x − y|=|x + (-y)|≤ |x|+|-y|...Females typically have two X chromosomes (46,XX), and males have one X chromosome and one Y chromosome in each cell. 47,XYY syndrome is caused by the presence of an extra copy of the Y chromosome in each of a male's cells. As a result of the extra Y chromosome, each cell has a total of 47 chromosomes instead of the usual 46.Problem 5 (p. 354 #9). Let X= min(S;T) and Y = max(S;T) where Sand T are independent Exp( ) random variables. Let Z= Y X. a) Find the joint density of Xand Y. Are Xand Y independent? [Hint: Consider the probability P(s<X<Y <t) expressed as a double integral of the joint density. What happens when you di erentiate this by sthen by t?]5.2.1 Joint Probability Density Function (PDF) Here, we will define jointly continuous random variables. Basically, two random variables are jointly continuous if they have a joint probability density function as defined below. P((X, Y) ∈ A) = ∬ A fXY(x, y)dxdy (5.15) P ( ( X, Y) ∈ A) = ∬ A f X Y ( x, y) d x d y ( 5.15) The function fXY ...E|XY|≤E1/r|X|rE1/s|Y|s ≡ X r Y s for r>1where 1/r +1/s = 1 defines s. When the expectations are finite we have equality if and only if there exists A and B not both 0 such that A|X|r = B|Y|s a.e. Proof. The result is trivial ifE|X|r =0or∞. Likewise for E|Y|s. So suppose thatE|X|r > 0. Now |ab|≤ |a|r r + |b|s s, as in the figure. Now ...

Built within Python are a set of “operators” that can are used to ask mathematical questions. > and < symbols are probably quite familiar to you. >= denotes “greater than or equal to.”. <= denotes “less than or equal to.”. == denotes “equals, though do notice the double equal sign! A single equal sign would assign a value.The X and Y chromosomes, commonly referred to as the sex chromosomes, are one such pair. They determine the biological sex, reproductive organs, and sexual characteristics that develop in a person. a) ∀x∃y (x^2 = y) = True (for any x^2 there is a y that exists) b) ∀x∃y (x = y^2) = False (x is negative no real number can be negative^2. c) ∃x∀y (xy=0) = True (x = 0 all y will create product of 0) d) ∀x (x≠0 → ∃y (xy=1)) = True (x != 0 makes the statement valid in the domain of all real numbers)X&Y is the third studio album by British rock band Coldplay. It was released on 6 June 2005 by Parlophone in the United Kingdom, and a day later by Capitol Records in the United States. The album was produced by Coldplay and producer Danton Supple. It is noted for its troubled and urgent development, as well as manager and creative director ... CAL Cargo Air Lines. Carmel Agrexco. Castro Model. Cellcom Israel. Ceragon Networks. Check Point Software Technologies. Cimatron. Clalit Health Services Group. ClickSoftware Technologies.Page couldn't load • Instagram. Something went wrong. There's an issue and the page could not be loaded. Reload page. 329K Followers, 1,330 Following, 816 Posts - See Instagram photos and videos from Dani Jackel (@danijackel)

What time costco closed today.

Noun. 1. XY - (genetics) normal complement of sex hormones in a male. sex chromosome - (genetics) a chromosome that determines the sex of an individual; "mammals normally have two sex chromosomes". genetic science, genetics - the branch of biology that studies …Homework 9 (Math/Stats 425, Winter 2013) Due Tuesday April 23, in class 1. The joint probability mass function of X and Y is given by p(1,1) = 1/8 p(1,2) = 1/4Free area under between curves calculator - find area between functions step-by-step.s! 3 ! 2 !2!2!1 0 1 2 corr = 0 Y 30 10 15 20 25 30 corr = 0.1 Y 30 10 15 20 25 30 corr = !0.1 Y 30 5 10 15 20 25 30 corr = 0.3 Y 30 5 10 15 20 25 corr = 0.5 Y 30 10 ...1) ∀x∃y: For every x there exists a y (such that...) 2) ∃y∀x: There exists a y (such that) for every x... Using the marriage example respectively: 1) Everyone is married to someone (ie. For every person there exists a person to whom he/she is married) 2) Someone is married to everyone (ie. There is someone who is married to everyone) Share.X&Y is the third studio album by British rock band Coldplay. It was released on 6 June 2005 by Parlophone in the United Kingdom, and a day later by Capitol Records in the United States. The album was produced by Coldplay and producer Danton Supple. It is noted for its troubled and urgent development, as well as manager and creative director ...

1. Yes, ∃x∀y(P(x, y)) ∃ x ∀ y ( P ( x, y)) means that there is a x x such that, for every y y, P(x, y) P ( x, y) holds. There is nothing peculiar here. The existential quantifier should always be read as if there was a "such that" after it. For instance, ∃x(P(x) → Q(x)) ∃ x ( P ( x) → Q ( x)) means that there is a x x such ...Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, Bikini,Tìm chi tiết và giá khoảng Bơi, Trang phục bơi từ Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, ...Mar 15, 2022 · It’s a gargantuan-sized car that starts at $120,990, provided you buy it in white, take the stock 20-inch wheels, and stick with a five-seat all-black interior. Meanwhile the Model X Plaid ... Free Gradient calculator - find the gradient of a function at given points step-by-step.McGregor’s X and Y Theories are contrasting theories that depict two different aspects of human behavior at work. Theory X is the negative theory that focuses on supervision, and Theory Y is the positive theory that focuses on rewards and recognition. Both are motivational theories and are used by managers to motivate their employees to ...In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such as a linear regression.A …This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 5, 0 ≤ v ≤ 1. Evaluate the surface integral.Split the string into two non-empty substrings at a random index, i.e., if the string is s, divide it to x and y where s = x + y. Randomly decide to swap the two substrings or to keep them in the same order. i.e., after this step, s may become s = x + y or s = y + x. Apply step 1 recursively on each of the two substrings x and y. Itô's lemma is the version of the chain rule or change of variables formula which applies to the Itô integral. It is one of the most powerful and frequently used theorems in stochastic calculus. For a continuous n-dimensional semimartingale X = (X 1,...,X n) and twice continuously differentiable function f from R n to R, it states that f(X) is a semimartingale …Linear Regression Formulas x is the mean of x values y is the mean of y values sx is the sample standard deviation for x values sy is the sample standard deviation for y values r is the regression coefficient The line of regression is: ŷ …1. (MU 8.1) Let X and Y be independent, uniform random variables on [0,1]. Find the density function and distribution function for X +Y. We will use a convolution equations to find the density and distribution of Z: f Z(z) = Z ∞ x=−∞ f X(x)f Y (z −x)dx F Z(z) = Z z u=−∞ f Z(u)du. Now, we use the fact that X and Y are independent ...

S: X: Y: The Chaldean numerology system is perhaps the oldest form of numerology known, with its origin in ancient Babylon. Every letter has a numerical value from 1 to 8. It has no letters attached to number 9, which is considered very spiritual. Using this letter in Chaldean Numerology is forbidden, as it is a great dishonesty.

Learning Objectives. 4.5.1 State the chain rules for one or two independent variables.; 4.5.2 Use tree diagrams as an aid to understanding the chain rule for several independent and intermediate variables.; 4.5.3 Perform implicit differentiation …Jul 7, 2023 · Copy Files and Folders Over the Network. xcopy C:\Videos "\\SERVER\Media Backup" /f /j /s /w /z. Here, the command is used to copy all the files, subfolders, and files contained in the subfolders [/s] from source of C:\Videos to the destination folder Media Backup located on a computer on the network by the name of SERVER. Relations are generalizations of functions. A relation merely states that the elements from two sets A. are related in a certain way. . that appear in the second coordinates of some ordered pairs. Under this convention, the mathematical notations ≤, ≥, =, ⊆, and their like, can be regarded as relational operators.The point (x, y) to annotate. The coordinate system is determined by xycoords. xytext (float, float), default: xy. The position (x, y) to place the text at. ... It's a tuple of relative coordinates of the text box, where (0, 0) is the lower left corner and (1, 1) is the upper right corner. Values <0 and >1 are supported and specify points ...March 30, 2023. The calculators below calculate the value of Sxx, Sxy, and Syy on the basis of the x data values and y data values entered. Simply enter the values of the x and y variables in the calculators below to find the Sxx, Sxy, and Syy values.Linear Regression Formulas x is the mean of x values y is the mean of y values sx is the sample standard deviation for x values sy is the sample standard deviation for y values r is the regression coefficient The line of regression is: ŷ …B; 2 x 2 x 2 x 2 2 x 2 x x x x x x 2x 0 Thus, x must be 0. 58. a line 59. part of the coordinate plane above the line y 2x 1 60. 1 2 4 8, so 1 2 in. 3 8 in. 61. 1 4 1 4 6, so 1 4 6 in. 1 4 in. 62. 4 5 1 8 0, so is 3.7 centimeters long.4 5 in. So,1 6 0 Gin. 63. 10 mm 1 cm 64. 2.5 cm 25 mm, so 2.5 cm 28 mm 65. 0.025 cm 0.25 mm, so 0.025 cm 25 mm ...Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-stepSolution. THEOREM 3 (a) Law of Absorption : yx+x = x. yx+x = yx+x1 by identity (Ax. 2b) = x (y+1) by distributivity (Ax. 4a) = x1 by Theorem 2 (a) = x by identity (Ax. 2b) THEOREM 3 (b): x (x+y) = x by duality. THEOREM 6 (a) De Morgan's Laws: (x+y)' = x'y'. Proof: We will prove that x'y' is a complement of x+y by proving that x'y' satisfies ...

Terraria lock chest.

Bridget childers instagram.

The Choose-an-Element Method. The method of proof we will use in this section can be called the choose-an-element method.This method was introduced in Preview Activity \(\PageIndex{1}\).Purdue's Department of Statistics is Indiana's major center for statistical teaching and research. It has the state's largest and oldest doctoral program in statistics and offers a broader range of statistics courses than any other institution in the state. The faculty is recognized as one of the nation's strongest in studies by the National ...Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax² + bx + c, crosses the x-axis. As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains. Over the line y = x: (x, y) (y, x) Through the origin: (x, y) (–x, –y) TRANSLATIONS: Translations are a slide or shift. Translations can be achieved by performing two composite reflections over parallel lines. Translations are isometric, and preserve orientation. Coordinate plane rules: (x, y) (x ± h, y ± k) where h and k are the ...E|XY|≤E1/r|X|rE1/s|Y|s ≡ X r Y s for r>1where 1/r +1/s = 1 defines s. When the expectations are finite we have equality if and only if there exists A and B not both 0 such that A|X|r = B|Y|s a.e. Proof. The result is trivial ifE|X|r =0or∞. Likewise for E|Y|s. So suppose thatE|X|r > 0. Now |ab|≤ |a|r r + |b|s s, as in the figure. Now ...Sep 8, 2010 · x>y, sqrt(x)>y, x^3>y all three represents the region below the graph for all three cases. We need to answer is x>y (1) sqrt(x)>y You are below the yellow line does not imply you are below the purple line. Insufficient (2) x^3>y Now x need not be just positive, but looking at the graph is enough to conclude this is not sufficient. Symbolab is the best step by step calculator for a wide range of math problems, from basic arithmetic to advanced calculus and linear algebra. It shows you the solution, graph, detailed steps and explanations for each problem.Tap for more steps... x⋅x+x(−y)+yx+y(−y) x ⋅ x + x ( - y) + y x + y ( - y) Simplify terms. Tap for more steps... x2 − y2 x 2 - y 2. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Split the string into two non-empty substrings at a random index, i.e., if the string is s, divide it to x and y where s = x + y. Randomly decide to swap the two substrings or to keep them in the same order. i.e., after this step, s may become s = x + y or s = y + x. Apply step 1 recursively on each of the two substrings x and y. ….

Relations are generalizations of functions. A relation merely states that the elements from two sets A. are related in a certain way. . that appear in the second coordinates of some ordered pairs. Under this convention, the mathematical notations ≤, ≥, =, ⊆, and their like, can be regarded as relational operators.With Joy Into The Rose Garden Dragon Blood The Seventh Reincarnation, The Rotten Daughter Hopes to be Happy This Time – In the Previous Life, Her Engagement Was Broken, But in This Life, She Was Doted on by Her Fiancé. Funeral Hidden Desire The Great Battle of Games The Villain’s Memories Revealed What To Do If The Heroine …I am asked to prove the following: Let s(x):= ∑∞ n=0(x n) s ( x) := ∑ n = 0 ∞ ( x n). Then s(x + y) = s(x)s(y) s ( x + y) = s ( x) s ( y). I don't know how to start. I am thinking about exp(x) exp ( x) function with ∑∞ n=0 xn n! ∑ n = 0 ∞ x n n!.Feb 21, 2018 · A Level Maths revision tutorial video.For the full list of videos and more revision resources visit www.mathsgenie.co.uk. Built within Python are a set of “operators” that can are used to ask mathematical questions. > and < symbols are probably quite familiar to you. >= denotes “greater than or equal to.”. <= denotes “less than or equal to.”. == denotes “equals, though do notice the double equal sign! A single equal sign would assign a value.Purdue's Department of Statistics is Indiana's major center for statistical teaching and research. It has the state's largest and oldest doctoral program in statistics and offers a broader range of statistics courses than any other institution in the state. The faculty is recognized as one of the nation's strongest in studies by the National ...R = {(x, y): x − y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by ( a ) R = { ( x , y ) : x and y work at the same place }Sep 8, 2010 · x>y, sqrt(x)>y, x^3>y all three represents the region below the graph for all three cases. We need to answer is x>y (1) sqrt(x)>y You are below the yellow line does not imply you are below the purple line. Insufficient (2) x^3>y Now x need not be just positive, but looking at the graph is enough to conclude this is not sufficient. Tesla Model 3 lifting jack pad - 4 pack with mesh carry bag. - Jack lifting pads - Use these lifting pucks to insure proper lifting of your Tesla and avoid any potential battery damage. -Made from a hard vulcanized rubber. 4 pucks are needed to use a two post lift. - Used to protect battery and paint - Locates in factory lifting locations to ...¨s x y s0 sn x0 xn y0 yn Figure 1: Rotating a curve about the y-axis. Surface area Consider the parametric curve x= x(t) y= y(t): Consider the surface formed by rotating the curve about the y-axis. The di erential surface area element is given by dA= 2ˇxds = 2ˇx(t) q (x0(t))2 + (y0(t))2 dt: The the surface area from time t 0 to time t 1 is ... S x y, Large variety of maps. You can find the full list at our condo generator page. The future of condo games is here., The XY sex-determination system is a sex-determination system used to classify many mammals, including humans, some insects ( Drosophila ), some snakes, some fish ( guppies ), and some plants ( Ginkgo tree). In this system, the sex of an individual is determined by a pair of sex chromosomes. In most cases, females have two of the same kind of ... , If f(x) is the density function for a random variable X, then we can represent y f(x) graphically by a curve as in Fig. 2-2. Since f(x) 0, the curve cannot fall below the x axis. The entire area bounded by the curve and the x axis must be 1 because of Property 2 on page 36. Geometrically the probability that X is between a and b, i.e.,, Females typically have two X chromosomes (46,XX), and males have one X chromosome and one Y chromosome in each cell. 47,XYY syndrome is caused by the presence of an extra copy of the Y chromosome in each of a male's cells. As a result of the extra Y chromosome, each cell has a total of 47 chromosomes instead of the usual 46., The investigation is ongoing. Anyone with information on the case is asked to contact Riverside County District Attorney Investigator Mario Moreno 951-955-9470 or Riverside County Sheriff's ..., Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, Bikini,Tìm chi tiết và giá khoảng Bơi, Trang phục bơi từ Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, ..., 5.2.1 Joint Probability Density Function (PDF) Here, we will define jointly continuous random variables. Basically, two random variables are jointly continuous if they have a joint probability density function as defined below. P((X, Y) ∈ A) = ∬ A fXY(x, y)dxdy (5.15) P ( ( X, Y) ∈ A) = ∬ A f X Y ( x, y) d x d y ( 5.15) The function fXY ..., Vector3. Class representing a 3D vector. A 3D vector is an ordered triplet of numbers (labeled x, y, and z), which can be used to represent a number of things, such as: A point in 3D space. A direction and length in 3D space. In three.js the length will always be the Euclidean distance (straight-line distance) from (0, 0, 0) to (x, y, z) and ..., Find Men's Bags & Backpacks at Nike.com. Free delivery and returns on select orders., Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Desmos | Graphing Calculator Loading... , Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, Bikini,Tìm chi tiết và giá khoảng Bơi, Trang phục bơi từ Sản phẩm mới, cô gái tùy chỉnh Sxy Polyester, ..., Table 2.4 summarizes the facts about the two types of quantifiers. "For every x, P(x) ," where P(x) is a predicate. Every value of x in the universal set makes P(x) true. "There exists an x such that P(x) ," where P(x) is a predicate. There is at least one value of x in the universal set that makes P(x) true., The Choose-an-Element Method. The method of proof we will use in this section can be called the choose-an-element method.This method was introduced in Preview Activity \(\PageIndex{1}\)., Written separately, they become: Each of these two solutions is also called a root of the quadratic equation. Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax² + bx + c, crosses the x-axis., a) ∀x∃y (x^2 = y) = True (for any x^2 there is a y that exists) b) ∀x∃y (x = y^2) = False (x is negative no real number can be negative^2. c) ∃x∀y (xy=0) = True (x = 0 all y will create product of 0) d) ∀x (x≠0 → ∃y (xy=1)) = True (x != 0 makes the statement valid in the domain of all real numbers), A Level Maths revision tutorial video.For the full list of videos and more revision resources visit www.mathsgenie.co.uk., 1) ∀x∃y: For every x there exists a y (such that...) 2) ∃y∀x: There exists a y (such that) for every x... Using the marriage example respectively: 1) Everyone is married to someone (ie. For every person there exists a person to whom he/she is married) 2) Someone is married to everyone (ie. There is someone who is married to everyone) Share., Geometrically, these roots represent the x-values at which any parabola, explicitly given as y = ax² + bx + c, crosses the x-axis. As well as being a formula that yields the zeros of any parabola, the quadratic formula can also be used to identify the axis of symmetry of the parabola, and the number of real zeros the quadratic equation contains. , MIỄN PHÍ VẬN CHUYỂN *CHO ĐH TỪ 499K ✓ THÔNG TIN VẬN CHUYỂN ✓ Mua hàng không tiếp xúc Giảm giá 10% ✓ Mua sắm SHEIN SXY NỮ tại SHEIN, tìm được giá cực rẻ., sex chromosome, either of a pair of chromosomes that determine whether an individual is male or female.The sex chromosomes of human beings and other mammals are designated by scientists as X and Y.In humans the sex chromosomes consist of one pair of the total of 23 pairs of chromosomes. The other 22 pairs of chromosomes are called autosomes. ..., Explore math with our beautiful, free online graphing calculator. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more., 1) ∀x∃y: For every x there exists a y (such that...) 2) ∃y∀x: There exists a y (such that) for every x... Using the marriage example respectively: 1) Everyone is married to someone (ie. For every person there exists a person to whom he/she is married) 2) Someone is married to everyone (ie. There is someone who is married to everyone) Share., Solve your math problems using our free math solver with step-by-step solutions. Our math solver supports basic math, pre-algebra, algebra, trigonometry, calculus and more., 18 thg 8, 2014 ... Addition photos from this shoot were featured in SnapMatter 2014 - Swimsuit Edition - Vol. 7., P x,y f X,Y (x,y) = 1. The distribution of an individual random variable is call the marginal distribution. The marginal mass function for X is found by summing over the appropriate column and the marginal mass function, This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Question: Evaluate the surface integral. S (x + y + z) dS, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 5, 0 ≤ v ≤ 1. Evaluate the surface integral., , Oct 27, 2015 · $S_{xx}$ is the sum of the squares of the difference between each $x$ and the mean $x$ value. $S_{xy}$ is sum of the product of the difference between $x$ its means and the difference between $y$ and its mean. So $S_{xx}=\Sigma(x-\overline{x})(x-\overline{x})$ and $S_{xy}=\Sigma(x-\overline{x})(y-\overline{y})$. , Step 1. Consider the surface integral ∫ ∫ S ( x + y + z) d S, S is the parallelogram with parametric equations x = u + v, y = u − v, z = 1 + 2 u + v where 0 ≤ u ≤ 4, 0 ≤ v ≤ 1., In statistics, Sxy represents the sum of the product of the differences between x values and the mean of x and the differences between y values and the mean of y. This value is often calculated when fitting a simple linear regression model by hand. We use the following formula to calculate Sxy: Sxy = Σ (xi – x) (yi – y) where: Σ: A symbol ..., #689 in Video Games (See Top 100 in Video Games) #15 in Xbox One Controllers #16 in Xbox Series X & S Controllers: Pricing : The strikethrough price is the List Price. Savings represents a discount off the List Price. Product Dimensions : 6.26 x 4.25 …, Let’s start off by supposing that we wanted the rate of change of \(f\) at a particular point, say \(\left( {{x_0},{y_0}} \right)\). Let’s also suppose that both \(x\) and \(y\) are increasing and that, in this case, \(x\) is increasing twice as fast as \(y\) is increasing. So, as \(y\) increases one unit of measure \(x\) will increase two ..., 0. Mark44 said: (1) doesn't make sense, because the domain is not just x and y. (2) does make sense, and is about what I said before. (3) is true, but I don't think that's the answer they're probably looking for. (4) there is no information given that x and y are distinct. Of course, for the relation "is shorter than", two things being compared ...