-4 (0,0), for (n1, n2) = for (n1, n2) = (1,0), (M – 1,0), (0, 1), and (0, N – 1), e[n1,n2] 1 otherwise

Q: Evaluate: a In(x + y) e-y. dy dx

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Q: Let D. be the linear transformation fromc (a, 6] into cla, e). Find the preimage of the function.…

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Q: are orthogonal on einmx/L, n = 0, ±1, ±2,... [-L, L] with norm equal to √2L.

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Q: to determine the circulation of F around C,,

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Q: a) Solve the initial value problem using Laplace transform IMUTM UTM UTM IM UTM TM UTML

A: First we take Laplace transform of given differential equation and solve.Then solve for inverse…

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Q: Let x = s e and y =t es. Compute the Jacobian

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Q: Find the orthogonal trajectores For: x² - y² = c

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Q: Use Cauchy to integrate the following T ez - e-z 24 dz

A: The integral  is :The main to evaluate the integral using the Cauchy formula

Q: particle moves along an with S-axis S= slt) position function velocity function and %3D VIt)= ŚIt).…

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Q: 2 w2 In(w) dw

A: To evaluate the integral ∫12w2lnwdw

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A: What is Antiderivative: In calculus, a differentiable function F whose derivative is identical to…

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Q: Distinguish briefly the Skewness and kurtosis

A: Skewness is a measure of symmetry where symmetry means equal proportion to the left and right to the…

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Q: Let a,b,c and d be constants. Use the rules of expected value to show that Cov(aX+b, cY+d) = ac…

A: In question, We'll proof that Cov(aX+b, cY+d) = ac Cov(X,Y). Using expected value. The solution is…

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Q: a) Find the value of + 1) tdt by using the substitution u = +1

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Q: Use Forward – backward Method to find the new ho, where - ho = 0.3, Po = 0.98,01 = 2.41 and a, = =…

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Q: Let a be a positive real number, and let a>>1. Show that the square root of (1+ja) is approximately:…

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Q: Find the inverse laplace of: 3/(s3+9s)

A: Ans: 1/3(1-cos(3t))

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A: As per the question, we are given a strain tensor eij, and our task is to verify whether the…

Q: . Let X and Y be continuous random variables. The joint PDF of X and Y is 12r*y 0<y<r < 1, f(r, y) :…

A: The joint distribution of (X,Y) is given by, f(x,y) = 12x3y0&lt;y&lt;x&lt;10otherwise So,…

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.