Evaluate |[[p(4z + 3y² + 2x)dV = {(x, y, z) | 0

Q: 1 Let f (x,y) =In Then f (1, – 1) =... 3x2+4y3 XX

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Q: Oz Aradom Variable(x) has the following cof FX(X) = (x³ + x) al find the pdf of X find Pro <xcot)…

A: Given that: The cdf of random variable X is given as: FxX=12X3+X      where 0≤X≤1

Q: Find V × (V × F) if F(r, y, z) = xyj+ 6xyz k.

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Q: (c) For any (a, y) E R?, let F(x, y) = (4x - 3y + 1, 3x +4y + 1). Then F is a similarity.

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A: Property of gamma function: Γ(m+1) = mΓ(m) ............. (1)

Q: Find V (V x F), if F(r, y, z) = 7e""i + 2xe"j- 3e""k.

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Q: Determine fr and fy from f(x, y) = x³ + x²y + xy² + y³ ○ fx = x + xy, fy = x + 2xy ○ fx = x² + xy,…

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Q: -If F= 3xyz' i+ 4x'y} – xyzk the find V (V-F) and V × (V × F) at (– 1,2, 1). Also verify that V…

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Q: Let X~U (0,0), then P(X > X²) is

A: Given that X~U0,θ fx=1θ-0=1θ, 0≤X≤θ

Q: Let f(x,y,z) = 2 In (xy+2). Find f(0,1,3), F(-1,-2,4 and F(2,1,-1).

A: We have a function f(x, y, z) = zln⁡(xy + z). We need to evaluate this function at three different…

Q: Find V x (V × F) if F(x, y, z) = xyj+ 6xyz k. V × (V × F) =

A: Given: Fx,y,z=xy j+6xyz k To find the  cross product of ∇×∇×F

Q: Evaluate (z – i) dz where C:y(t) = VE² +1 + it³, 0<t < 1

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Q: Find fx and fy for f(x,y) = y In (x + 8y). II

A: Step 1:​f(x,y)=yln(x+8y)​Step…

Q: Evaluate SSS 5el=²+g²+z?)*² dV over B where B = {(r, Y, z) : z² + y² + z² < 1}. Take 7 = 3. %3D

A: A triple integral involves the integral with respect to the product of the variables x,y, and z. In…

Q: Evaluate SSS10e=²+y²+z?)"* dV over B where B = {(x, y, 2) : æ² + y² + z² < 1}. Take T = 3. Türkçe: B…

A: Triple integral is used to integrate the function of three variable over three dimensional region.…

Q: Let f(x, y) = √150 – 4x² – 2y² Evaluate f(1, 1) vad

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Q: Let f(x, y, z) = yexyz², then fxz is: Select one: O (4xyz + 2x²y³z²)exyz² O None of these O (2xy² +…

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Q: Find ¹₁ (5z + 2y)dA where D = {(2, y) | z² + y² ≤ 16, z ≥ 0}

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Q: Evaluate (r(t) · r1 t))l-2 where r1(t) = (t³, t“, t³), r(2) = (0, 3, 1), and r' (2) = (2, 4, 5) 42 O…

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Q: Let X and Y be independent and distributed as N(mu, 1). Is T=X-Y sufficient?

A: According to factorization theorem, if the likelihood function Lx,θ can be expressed in the form.…

Q: Find fx and fy for f(x,y) = y In (x + 8y). II

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Q: Let f(x, y) = 6e sin(7y) af af dy

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Q: Let S={(x,y)∈N×N|(2−x)(2−y)<2(4−x−y)}.Prove that S=TS=T, where T={(1,1),(1,2),(2,1),(1,3),(3,1)}

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Q: Let f(x,y,z) = x² e Vy*+ Compute f(3, - 5,3) and f(5,8, - 6).

A: Given that     f(x,y,z) = x2 e√(y^2+z^2)

Q: Find fx and fy for f(x,y) = y In (x + 8y). || fy = y x+8y

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Q: Let F(x, y, =) = (6x° In(5y² + 9) + 4=5) i + ( 10yx + 7:)j + (20xz4 + 7y – 37 sin 72) k 5y2 + 9 and…

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Q: Find X only using Crammers rule 2x+リ-「Z=D2 x2 -y +VZ 2 x? +2y +VN= 4

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Q: 4 Find f. (x, y) and f,(x, y) for f(x, y) = (5a³ – 4y²)*. f.(x, y) = Preview f,(x, y) = Preview

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Q: For f(x, y) = xe**Y, find fy (1, In 2) O 2 O 2 In 2 O 4 In 2 +2

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.