Show that a function f : R2-R defined by f(x,y)= x3- y3 / x2+ y2, if (x,y) is not equal to (0,0)  and f(x,y)= 0, if x=y=0 is continuous at (0,0).

Q: The differential equation Exact Bernoulli Separable Homogeneous (x² + y² ]y² = xy is

A:

Q: (A) Evaluate" [(x² + y)dx + (x + 1) 1+ along the path ABCA shown in figure C(0,3) A(0,1) x=3sint…

A:

Q: Use the information from the preceding table to fill in the following table. Year 2017 2018 2019…

A:

Q: Exercise 8.4.19. For each of the following functions, either prove that it is onto, or prove that it…

A:

Q: Determine f(x) = -4.

A: To find the value of x for which the function has value f(x)= -4 :-

Q: nom of how many (b.) how many If I is a finite set with an elements, elements does P(7.²) have?…

A: What is Power set: Roughly, a power set of a set is nothing but the set of all subsets of that very…

Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A:

Q: Prove that div(x) .curl - curl w functions. 11 where and ware vector

A:

Q: There is a worldwide shortage of nurses that is projected to be 20% below requirements by 2020.…

A: We need to calculate the percentage of schools that had an increase in application using the given…

Q: Let Z[i] = {a + bi : a,b ≤ Z}. This ring is called the Gaussian integers. Prove that Z[i]/(5) ≈…

A: x2+1=(x-2)(x-3) over  Z/5Z. and so by the Chinese Remainder Theorem…

Q: 2.2. Given a set of three data points {(0,1), (2,5), (4,17 } Determine Newtons interpolation…

A: We need to determine Newton's interpolation polynomial. Given: x y x0=0 y0=1 x1=2 y1=5 x2=4…

Q: Suppose 2.8 liters of water come out of a faucet each minute. For how many minutes was the faucet on…

A:

Q: Consider the following initial-value problem i=x²-2r+t-1, 0≤t≤2, x(0) = 1. Use two steps of the…

A:

Q: Consider the function f(x, y, z) = xy + y² +². (a) What is the gradient grad f of f, and what is its…

A: (a) Consider the given function, fx,y,z=xy+y2+z2 Here we need to find the gradient of f and its…

Q: 1.2. what is the decimal equivalence of binary number (101000002 the

A:

Q: Draw a direction field for the given differential equation and determine the behavior as ?→∞. If…

A: Given, The differential equation is  y ' = −y(5 − y).   We have to draw direction field for the…

Q: Verify that the indicated family of functions is a solution of the given differential equation.…

A:

Q: 3 most important rules or ideas or “key concepts” about research.

A: 3 most important rules or ideas or “key concepts” about research are : 1) first one is measurement…

Q: Problem 4: Define freedholm, Volterra and Singular integral equation. Show that the function 1 g(x)=…

A:

Q: Let the basis vectors be given by a = [3,1] and 6 = [3,3]. Give the image of a general coordinate…

A:

Q: please help! see image

A: Let, g(x) = a|x - h| + k.  Now, from the graph, we see,      g(-8) = g(4) = 7. Then, a|-8 - h| + k =…

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z =…

A:

Q: Differential Equations Find the Particular Solution of y(2x2-xy+y2)dx - x2(2x-1)dy = 0 when x=1 ,…

A:

Q: integra

A:

Q: C ywiru login-search McGraw Hill Campus…

A: a )  Probability of card drawn is diamond = Total diamond card / Total card = 13/52 = 1/4

Q: : Prove that three dimentional volume element "dx dy dz " is not invariant bu ment is invariant…

A:

Q: Linear Programming "The Possibility Restaurant Hazel and were food and nutrition majors at State…

A: let fish dinner be x1 and beef dinner be x2 objective function Max z=600x1+800x2 according to…

Q: Find the indicated nth partial sum of (Sn) if the arithmetic sequence. a) -3 + -3/2 + 0 +…+30 b) u2=…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: Diagonal elements of Cholesky factor. Each X ES+ has a unique Cholesky factorization X = LLT, where…

A: Given That : Each X∈Sn++ has a unique Cholesky factorization  X=LLT where L is a lower triangular…

Q: And what are the domain and range?

A: according to question,  (i) If given graph is a function then state the domain and range of the…

Q: Use the Venn diagram and the given conditions to determine the number of elements in each region, or…

A:

Q: (a) If 4-[a] is a 3x3 matrix; such that a -i (4-7), find the values of diagonal elements and the…

A: What is Matrix: If we arrange some elements, may be number or alphabets in rectangular array, the…

Q: 44. How many terms do we need be accurate within 5 decimals for the series A. 15 terms B. 12 terms…

A:

Q: Rewrite the following phrase utilising a solitary power series whose basic meaning includes…

A:

Q: Solve the initial value problem ex (x²y² +4x³y² + 1) dx + (2x4 ye* + 2y) dy = 0, y(0) = √5

A: Given differential equation is ex x4 y2 +4x3y2 +1 dx + 2x4 y ex +2y dy =0   with  y0=5   Note:- A…

Q: Give an example of a tautology. Give an example of a contradiction. Explain your answers.

A: A sentence is said to be tautology if it is always true. A sentence is said to be a contradiction…

Q: cy² = x² + y

A:

Q: 2) Find (if possible) the values of a,b,c such that the system of linear equations has: a) unique…

A: Solution:

Q: 2. Find the fi K(x, t)

A:

Q: A total of 17,000 students entered Big State University in the fall of 2013. The following table…

A:

Q: 5. Mrs Kiran purchased the following items from New Style Garment Store, Karol Bagh, Delhi on 7…

A: We have to evaluate the amount of money Mrs. Kiran gets back when she gives Rs. 1700 to the…

Q: Question 2 using X foc) appropriate Lagrange interpolationg polynomial the following tata table O 1…

A:

Q: A tank shaped like a right circular cone with radius 5 meters and height 15 meters is filled with…

A: What is Derivative: Physically, the derivative of a function represents in which rate a function…

Q: Convolution with Impulse (Dirac) Function. Convolution with impulse function can be performed by the…

A: Note: The value inside the circle is incorrect. The proof for the correct value is given in the…

Q: Use finite approximations to estimate the area under the graph of the function f(x)=3−x2−2x between…

A: The Given function is, f(x)=3-x2-2x  Between x=-3 and x=1 Here we have to find the area under the…

Q: 2. Given that f(x) = 2x-3 and g(x) = 9x²–5x+11, determine the following: a. g(x) − f(x) = - [K2] b.…

A:

Q: 1- y"+y'-2y = x² + e³x what is the particular (nonhomogenous) solution of the given ode? OA) Y =…

A:

Q: SOLVE STEP BY STEP AND IN DIGITAL FORMAT 5. Draw the graph G that has as vertex set V (G) and edge…

A: What is Graph: The study of graphs, which are mathematical constructions used to represent pairwise…

Q: 2. Analyze the solution to the following optimal growth model using a phase diagram drawn in (k, μ)…

A: Consider the given model, Vk0=max∫0∞e-ptlncdt subject to, k˙=k1-α1-α-c-δk, k0=k0, and kt≥0. So, for…

Q: For the following graph find the fourier series? Ans 2x 2 sin 4x 3 sin6x + 3.5 5.7 + -.) f(x)

A: What is Fourier Series: A Fourier series is a trigonometric series that includes sine and cosine…