5. Evaluate the path integral [1 F. dr where F(x, y, z) = (3x²yz − 3y)i + (x³z − 3x)j + (x³y + 2z)k and C is the helix with initial point (0, 1,) and terminal point (-1,0, π) defined by r(t) = cos(t), sin(t), t>. (538831889)

Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

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Q: Let F(x, y) = x2 + x² + y2J- (a) Show that F. dr +| F. dr if C and C2 are the semicircular paths…

A: The function given to us is  F(x,y)=yx2+y2i-xx2+y2j

Q: Consider any(n) + an-1y(n-1) + + a1y' + aoy = f(x) where an, ...a1, ao E R, where an 7 0. ... (a)…

A: consider anyn+an-1yn-1+.....+a1y'+a0y=fx            ...i where an, ......., a1 , a0∈ℝ where an≠0 (a)…

Q: (2) Let F(x, y) = (cos(y)+2x, -x sin y+1). Show that F is path independent by finding %3D a…

A: For the given vector function to be independent, it must be derived from a potential scalar function…

Q: 4. Perform the indicated multiplication of the two differential operators: (D –x)(x²D– 2x).

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Q: 5. Find the work done by F = (x² + y)i + (y² + x)j + ze²k over the following paths from (1, 0, 0) to…

A:

Q: 1) Find the linearization L(x) of f(x) at x = a. f(x) = 2x2 + 4x - 1, a =

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2. Let closed curve C consist of the line segment from (0,0) to (2, 1), followed by the line segment…

A: We will solve both the parts using the basics of integral calculus, in particular double integral,…

Q: Determine when the following pairs of functions are linearly independent. (a) y1(t) = e"it; Y2(t) =…

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Q: f (x, y) is a differentiable function with Vf(4,3) = 7i+ 5j. 2. Suppose w = (a) Find the directional…

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Q: (1) (a) Show that the line integral tan(y) dr +x sec (y) dy is independent of path, where C is any…

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Q: Let sin(4x + 7y°) x3 + y5 if (x, y) # (0,0) f(x, y) = 0. if (x, y) = (0,0) %3D Which of the…

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Q: Find the tangential and normal components.  r(t)=(t+1)i+2tj+t^ 2 × k     ,   t = 1

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 6. Let f(x,y) = sin(x + y) + arcsin (xy) a. Find the linearization L(x,y) at the point (0, ")

A: We have to find linearization of given function f(x,y): Concept: The linearization of a function…

Q: 7. Which of the following sets of functions is linearly dependent on R0,2? (a) {6, z, sinz} (b) {1,…

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Q: Integrate the function f(r,y, z) = Over the entire 3D coordinate system, i.e., all of R'.

A: We have to integrate the function fx, y, z=1x2+y2+z21+x2+y2+z2 over the entire 3D coordinate system,…

Q: Write the system x'= e"x – 4ty+9 sin(t), y' = 7 tan(t)y + 9x – 4 cos(t) in the form = P(t) + F(t).…

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Q: 6.(6 pts) Evaluate the line integral / (x+ y + 2) ds along the curve C given by r(t) = (sin t, cos…

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Q: Integrate f(r, y, z) = for 0 <t< V3. + y² over the curve r(t) = [cos(t) +t sin(t), sin(t) – t…

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Q: Suppose F(x, y) = −y sin(x)i + cos(x)}. (a) Find a vector parametric equation for the parabola y =…

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Q: Find the line integrals of F = 2yi + 4xj + zk from (0,0,0) to (1,1,1) over each of the following…

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Q: 9.) A particle moves in a straight line according to the law of motion: s=cos(x). a. Find the…

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Q: : Mark all the ODEs in the list for which the function y(t) = cos(t) is a solution. A) y' = sin(t)…

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Q: Check cosh(xz)(z dx + x dz) for path independence. Does cosh(xz)(z dx + x dz) have path…

A: To verify whether the function cosxzzdx+xdz is path independent or not…

Q: Evaluate the path integral SF. dr, where F(x, y) = yi + xj and C is the line segment from (0, 0) to…

A: The given problem is to evaluate the given path integral of the vector field in the given path of…

Q: 2. Let closed curve C consist of the line segment from (0, 0) to (2, 1), followed by the line…

A: We will solve both parts of this question using basic knowledge of line integrals and definite…