Q/ If the joint p.d.fof X and Y as f(x,y) = }**y (cx?y ,x?

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Q: Can you explain the question step by step

A: Given: z = f (x,y) , x= e^s.cos(t) ,  y= e^s.sin(t)

Q: f"Ve-1) de (e* a) (e ) da Ante 1) de Bos birak

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

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A: Introduction: The trapezoidal rule is a method to approximate a definite integral numerically. In…

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A: Let us consider Irwin-Hall distribution as follows: Let X1, X2, ...., Xn be a random sample of size…

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Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

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A: For a function in several variables, partial derivative with respect to one variable say x can be…

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A: In this question, the concept of line integral is applied. Line Integral The function to be…

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A: To verify the given relations between partial derivatives.

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A: Consider the given graph. fx=x2+0.0001 Now, draw the graph.

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Q: Use RK2 (Heun's method) with ħ = 0.5 to estimate y(1) given o: 8 Vū, y(t = 0) = 8, y' (t = 0) = 2.…

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A: Given that zx,y=eyFexy where F(t) is differentiable function . Prove that xzx+yzy=yz

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Q: Let f(r, y) be a continuous

A: Introduction: A global extremum, also known as an absolute extremum, is the lowest or highest point…

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A: First find the partial derivative of the given function with  respect to x :

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A: We know, sin z = sin x cosh y + i cos x sinh y, Where, cosh and sinh are hyperbolic functions.

Q: If z = y + f(x^2-y^2), where f is differentiable, show that y(∂z/∂x) + x (∂z/∂y) = x.

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Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: Use the linear approximation to ƒ(x, y) 12x² at (3, 9) to estimate f(3.1, 8.8). y2+7 (Use decimal…

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Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: