Show that the following equation is exact and solve it: (2y sin x cos x - y + 2y² exy²) dx - (x - sin² x - 4xyexy²)dy = 0

Q: For a matrix A, define the eigen-vector as a non-zero column matrix X and eigen-value a scalar ›…

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Q: f(x) = 3.1.³ et 1. Using the laws of Calculus, provide the expression for f'(x)- which will be our…

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Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: a) In the given graph the four vertices A, B, E and F are of odd degree,hence by the Eulerian Graph…

Q: Use Laplace transform to solve the partial differential equation: d²u du du(x,0) t> 0, 0<x<1, u(x,0)…

A: Solution

Q: Find the total area of the region satisfying the E

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Q: Calculate - 2x²y dx + 2xy² dy, where C is the circle of radius 3 centered on the origin. use this…

A: Given that, Pdx+Qdy=-2x2dx+2xy2dy, Therefore, P=-2x2y, and Q=2xy2, Thus, need to use Green's Theorem…

Q: 3. A probability mass function for a particular random variable y having nonnegative integer values…

A: We obtained the pmf and moment generating function. The detailed solution is attached below.

Q: 7/ Find the optimal solution of the following (T.P) by using Least-Cost method. 6 40 50 70 90 90 100…

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Q: Find the chromatic polynomial of G

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Q: Evaluate the characteristic w" + k ² x ²³w = 0 value of k in the following differential equation w…

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

Q: TASK 2: Prove that if G is a group and a, b = G, then (1) o(a¹ba) = o(b) o(ab) = o(ba)

A: These two results follow by proving G is abelian. We present the detailed solution in the next step.…

Q: 2. If a is an involution, then Baß is an involution for any transformation B.

A: It is given that α is an involution. So, we can say that α2=I.

Q: z+y <=0. (a) Using - definition, show that lim (a)+(0,0) 2²+ y² +1 [2²sin +3² sin, (2, 3) (0,0) (b)…

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Q: 1.a) Apply the Trapezoid and Corrected Trapezoid Rule, with h =, to approximate the integrale-2x²…

A: (a). Given integral is ∫13e-2x2dx. The step size is h=18. We know that the integral of a function fx…

Q: Show if x, is convergent or divergent T.3 'n sin(x) dx 1+x S'

A: Introduction: The convergence or divergence of an infinite series depends upon the sum of the…

Q: (ylny-exy)dx + ( + xlny) dy = 0

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Q: Instruction: Setup the iterated double integral that gives the volume of the following solid.…

A: Construct a prism

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: First find the degree of all the vertex.  The degree of vertex  V of a graph is the number of edges…

Q: For a data set of size 10, the highest order of a polynomial that could be fitted using Least…

A: Inbtroduction: The least square approach involves minimising the sum of the squares of the points'…

Q: Let What is the rank of AT A? Answer: A 3 0 0 0 0 0 5 11 −4 0 3 6 5 2 0 0 3 6 2 0 0 0 8 0 0 00 0 0

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Q: Use Laplace transform to solve the partial differential equation: o²y_by -+xt where y(x,0) = 0,…

A: Solution

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: A connected graph G is said to be Eulerian if the graph G has a Euler circuit. A graph has an Euler…

Q: Solve using Gauss-Seidel Iterative Method

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Q: x²-x+z Evaluate SS do, where o √2+4y² S is the part of the surface z = y² + x that lies inside the…

A: as given z=y2+x differentiate with respect to x zx=1 differentiate with respect to y zy=2y…

Q: How many 7-letter words contain exactly 2 vowels? (For example, an 8-letter word with 5 vowels is…

A: To find the number of words contain exactly two vowels :-

Q: Volume of Solid Revolution(Circular Disk and Washer Method) Find the volume of the solid generated…

A: given curve x2+y2=4 find the volume of the solid generated by revolving the area bounded by the…

Q: Find symmetric and parametric equations of the line through the two points (−3, 5, 2) and (1, −3,…

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Q: (b) Use Newton's method to construct a sequence of rational numbers con- verging to √2. Google…

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Q: 2. 2y (x²-y tx) dx-(x²-2y) dy = 0

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Q: 2. f (t) = sin ( € - 2π) H ( t - 21)

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Q: If f(x) is a polynomial of degree <3, f(a) a x-a

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Q: In Exercises 9 to 12, determine whether the two graphs are equivalent. 12. F с A B C D E BADO В E A

A: The given two graphs are not equivalent

Q: 11. Carry out a single-variable search to minimize the function 12 f(x) = 3x² + on the intervalers!…

A: Given function is  f(x) = 3x2 + 12x3  on the interval 12≤x≤52.(a) Golden search method: First…

Q: برهن على صحة التكاملات التالية : fx²J, (x) dx = x²3, (X) + x1(x)-[Jux) dx J, [x*J₁ (x) dx = x* J,…

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Q: Use Laplace transform to solve the partial differential equation: 8² y dy dx² at +xt where y(x,0) =…

A: Solution

Q: (1) Using Legendre polynomials, find linear least-squares approximation to f(x) = In|xl.

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Q: →Step 1 Given- 5 9 -3 4 1 -1 -7 -7 4 -3 65 -21x1 X2 X3 X4 ช 2 -7 2 3 | -107 9 -2

A: Solution

Q: 2Fs1 ² f (x, y) dx² proof. (H-w-) 2 ./ = P√= f (gy) - P²Fs (Psy) ар(х,у) 0 as x If f (x,y) → 2

A: Introduction: A Fourier transform (FT) is a mathematical transformation that decomposes capabilities…

Q: In Exercises 15 to 22, (a) determine whether the graph is Eulerian. If it is, find an Euler circuit.…

A: (a) Consider the given graph, Eulerian Graph theorem: it states that an Eulerian trail exists in a…

Q: (b) Find the Fourier-sine transform (assume k ≥0) for 1 f(x) = x + x³

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Q: 6. Determine the Poisson brackets formed from the components of the angular momentum L.

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Q: situation. and tell whether it is application on logarithmic function, inverse trigonometric…

A: As the policy of bartleby the provisions is to solve only one question at a time

Q: ) Solve by using Laplace transform the partial differential equation 2², a² y dt² =9. ox² y(0,1)= 0,…

A: Solution :-

Q: prove that every subset of negligible. set is negligible.

A: I have used definition of negligible set.

Q: bz+ bz=c, b0, be a line in the complex plane, w the reflection of the point through the line then

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Q: SD a strongly connected graph? D: W

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Q: (ylny – e¯xy)dx + ( + xlny) dy = 0

A: Solution :-

Q: S 5 1 1

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Q: A probability mass function for a particular random variable y having honnegative integer values is…

A: The pmf and mgf is calculated below.

Q: Use Laplace transform to solve the partial differential equation: d²u d²u du(x,0) = t> 0, 0<x<1,…

A: Solution