III. Find the mass of the wire in the shape of the curve determined by vector-valued function 8 3 1 R(t) = (tz, t?, 8t + 1),0 < ts1 3 if the density at any point (x, y, z) on the curve is 8(x,y,z) = z + /2y

Q: 1. f(x, y) = 1+ 2x/y, (3,4), v= 4î – 3ĵ |

A: According to our company policy we can answer only first question and rest can be reposted. Thanks

Q: 2 = 8 at the

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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: Find a vector-valued function r(t), that represents the following curve. Be sure to include an…

A: The vector valued functions in the parametric form can be represented as:…

Q: Sketch the level curves f(r,y) = c of the function f(x,y) = ln(r² + y²) for c = -1,c = 0,c = 1,c =…

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Q: Let r(t) = (e", e", te") be a vector function. Find; 21 -2t (a) r'(1) (b) r"(1) %3D

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Q: . Let n 2 3 be an odd number and f(a, y) = (x" + y")'/n. (a) Determine if f(x, y) is differentiable…

A: We will only use the basic knowledge of the differentiability of functions of two variables to…

Q: QI.a) In R",the circular cylinder x+y= 36 is intersected by the plane y +z= 6. find a vector valued…

A: Q.1 (a) we have given that in R3 the right circular cylinder x2+y2=36 by the plane y + z=6  we have…

Q: A new flag pole for a school campus measured 25 2/3 feet. It was put 4 1/2 feet into the ground and…

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Q: \(d\) is a metric on \(X\). Show that \(\rho : X^2 \to [0,\infty)\) defined by \[ \rho(x,y) =…

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Q: Let z = g(x, y) = f(3 cos(xy), y + ev) provided that f(3,6)= 7, f₁(3,6) = 2, f₂(3,6)= 5. i) Find g₁…

A: note :Since you have posted multiple questions, we will provide the solution only to the first…

Q: g(x,y,z)=x^2+y^2+(z-3)^2

A: For (a), We need to find the equation of the tangent plane to the level set g(x, y, z) = c at the…

Q: 1. Find a vector valued function that represents the curve of intersection of the semi-ellipsoid x²…

A: The equation of the semi-ellipsoid is The cylinder is

Q: Find a unit normal vector to the surface 6x2 + 2y2 + z2 = 225 at the point P : (5, 5, 5), and…

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Q: Q1.

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Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

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Q: Consider the function f(x, y) = x³+2xy+y. (a) Give the linearization L(x, y) of f at (2,3). (b) Use…

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Q: For the function f(x, y) = 2x² – 3xy + 8y² + 2x – 4y + 4, find a tangent vector to the level curve…

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Q: ar function = (1, 1, 2) i

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Q: Find the directional derivative of the function f(x, y, z) = xe³ + ye² + zeª at the point (0, 0, 0)…

A: The given function is:f(x,y,z)=xey+yez+zex

Q: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: Q1. Find the vector function r(t) given that r(0)= i+2j. and r'(t)= (2et, 3t², 4 cost)

A: The given data is: r0=i+2jr't=2et, 3t2, 4cost Find the vector function rt