2. Show that the given vector functions are linearly dependent on (-0,00). e' x(t) = x, (t) = 4e 2e2 8e?

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A: Given  a t=4t,5 sint, cos 3twe know that,v→t=∫a t dt +C1r t=∫vt  dt  +C2 ∴v→t=∫4t, 5 sint, cos 3t…

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A: The given equation is: ux,y=2020xy  The given function is a solution to Laplace's equation.

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Q: A point, p, is moving with acceleration 6t j - k at time t. If at t 1, the coordinates of P are (1,…

A: Answer

Q: Find the derivative of the vector function r(t) = In(13 – t²)i+ y13+tj– 9e 3 k r'(t) = {

A: The given vector function is                                   r(t)=ln13-t2i+13+tj-9e-3tk

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A: To determine the vector equation of the tangent line.

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Q: Show that the function f(x; y; z) = 2z3- 3(x2+y2)z  satisfies the Laplace equation.

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A: The detailed solution of the problem is given in the next steps.

Q: Find the derivative of the vector function r(t)=ln⁡(7−t^2)i+sqrt(8+t)j−5e^(2t)k r′(t)=⟨  ,  ,  ⟩

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A: Solution-

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Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

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Q: 4. Show that the covariant derivative of the metric tensor vanishes: V,gjk = V,gk = 0.

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Q: Find the derivative of the vector function r(t) = In(4 – 2) i+ v6+ij+7e¬6i k -

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, −12t) (a) If R(0) = (-1,4,-5),…

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Q: The two functions y1(t) = sint cos t and y2 (t) = sin 2t are linearly Independent. True False

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Q: Solve the initial value problem for ř as a vector function of t 1 = 8i + 8j -32k r(0) = 100k dt

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Q: 6. Suppose that the temperature T at point (x, y,z) is given by the function T = 2x2 – y? + 4z², and…

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Q: Find the derivative of the vector function r(t) = In(5 – t²)i+/16 +tj+ 7e 8t k r'(t) = (

A: Given vector valued function is rt=ln5-t2i+16+tj+7e-8tk