dV where V = dt y- x x= 2t, y = 5t, and z = t. Use the Chain Rule to find x+z' av dx (Type an expression using x, y, and z as the variables.)

Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: a) Show that the work performed by a constant force (not necessarily in the direction of motion) can…

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Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: aくtく2 -6(ft) whee f(t)=$°. e" 25t * X(ult-aJca(t-z)

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Q: [15] (2) Consider the function f: R² → R, f(x, y) = x² − 2xy + 2y² Determine Vf. a) b) c) d) GIVEN:…

A: Sine you have posted a question with multiple subparts we will solve first three subparts for you.…

Q: If/Given that → F(t)=(5t+3,3t²,8-4t³), Find: - a) The first derivative: b) The first derivative: c)…

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Q: 6. Find a vector which is normal to the currive: 3= 11 at (1,2). x³ + xy + y²

A: We have to find a vector which is normal to the curve: x³ + xy + y³ = 11 at (1,2).

Q: 2y dr - y dy y (x-2y) dy, y(0) =-1 O x = 2y - e +3 %3D a y = 2r- e+3 0x= 2y-e+3 O x = 3y + 2e +1

A: Given DE is 2y dx-y dy=y(x-2y)dy ⇒dx-12dy=12(x-2y)dy⇒dx=121+x-2ydy⇒dxdy=12+x2-y⇒dxdy+x-12=12-y Which…

Q: The following r(t) = (3 sint, 4 cost) represents vector-valued function. i) ii) iii) By eliminating…

A: The followingr(t)=(3sint,4 lcost) represents vector-valued function.i) By eliminating parameter 1,…

Q: For z = e"v In(ry): - Find the gradient of z when r= and y = 2 - Find the directional derivative of…

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Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Given: f(x, y) = 3x² – 2y² at (-,0) in the direction from P(-,0) to Q(0,1). . What is the unit…

A: The given problem is to find unit vector of the function in which direction from point P(-3/4,0) to…

Q: Let f(x, y, z) = xy + 2². In this problem, we find the directional derivative of fat (0, 2,5) in the…

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Q: Prove that Serret-Frenet formulae can be written in the from t' = dxt. n'=dxn, h' = d x b and…

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Q: Suppose z is implicitly given by the equation x³y-yz²+ -5 x In a neighborhood of the point P(1, 1),…

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Q: Find the vector equation for the line of intersection of the planes x + y - 4z = 4 and + 4z = -2

A: We have to find the vector equation.

Q: Be z = (x-y)/(x+y), where x = (u/v), y = (v2/u), calculate ∂z/∂u and ∂z/∂v

A: The given equation is z=x-yx+y where, x=uv, y=v2u. Find the value of ∂z∂u and ∂z∂v. Here we use the…

Q: Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find ∂z/∂t.

A: Solution:- The given question is  Let z = ƒ(x, y), x = g(s, t), and y = h(s, t). Explain how to find…

Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

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Q: ∠S and ∠Y congruent or supplementary

A: Given,           To find ∠S and ∠Y congruent or supplementary.

Q: Find the directional derivative of the function f(x,v) at point p in the direction of vector a. 1)…

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Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,

Q: Find (∂z)/(∂s) and (∂z)/(∂t), given: (a) z = x2 - 2y2 ; x = 3s + 2t, y = 3s - 2t

A: It is given that,            z = x2-2y2  ;  x = 3s+2t  ;   y = 3s-2t We have to find  ∂z∂s  and…

Q: Let f(x,y,z)=xyz. What is the directional derivative of f in the direction of the unit vector…

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Q: 3. Let f : R" → R be defined by f(x) = }||x||². Compute the following: a) Vf(x) b) The directional…

A: Euclidean norm: For any x=x1, x2, ⋯, xn∈ℝn, euclidean norm of x is defined by, x=x12+x22+⋯+xn2…