A). Suppose z=f(x, y), where x = g(s, t) and y=h(s, t). Find: d²z (1). [Verify using Mathematica] dt² d²z Əsət . [Verify using Mathematica

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A: In order to compute the derivative of the vector-valued function: Differentiate the vector function…

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Q: a) Find the directional derivative of f(x, y, z) = x²yz + 4xz² at (1, -2, 1) in the direction 2i - j…

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Q: Find (url and dive rgence the of F(xy2)=Xy2 i+ 2x Y j t z(os xyk.

A: Given: F(x, y, z) = xyz i + 2xy j + 2cosxy k To find: Curl and divergence of the given function.

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Q: Jx"(x* +2)"³ dx

A: We will find out the required value.

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Q: Let f (x, y) and g(x, y) be functions of two variables withthe property that ∂ f/∂x= ∂g/∂x and ∂…

A: Given: f(x, y)  and g(x, y) be functions of two variables with the property that ∂g∂x = ∂g∂x and…

Q: Suppose X1, X2 ∼ Unif(0, 1) and are independent. Let Y = min(X1, X2). Find fY (y).

A: We have given that X1,X2∼U(0,1)Objective :To find the  PDF of Y=min(X1,X2)

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A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

Q: prove that t1 = T2 is a necessary and sufficient condition for the unit function Id: (X, t1) → (X,…

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Q: 1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

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Q: дz x² + y², x = 2x + 3t and y = s + t. Find and in two ways: Ət Let z = x дz əs (a) By Chain Rule.…

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Q: Let f(x, y) = 6x – 2ry and the point M(5, 9). Among all unit directions, there is a unit direction…

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Q: Calculate the rectangular approximations R1, R2, and R4 for f(x)=2x−1 over the interval [1,5].

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Q: 2 Consider the vector-valued function R(t) with Ả'(t) = (sec²(t – 1), √t' (a) Find R(t) given Ả(1) =…

A: a) Given: R'→t=sec2t-1, 2t, -2 and R→1=1, 0, -1 To find: R→t

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Q: Find the directional derivative of f(x, y, z) = x²y²z + 4xz at (-1,2,1) in the direction 2i + j +…

A: We have to find the directional derivative of f(x, y, z)=x2y2z+4xz at (-1, 2, 1) in the direction…