1. (Section 17.2, 17.3) Find the work done by F(x,y) = -2yi-2zj in moving a particle along y - 4-2r² from (0, 4) to (2,-4) by: (a) using the parametrization of the curve to evaluate the work integral. (b) showing that the vector field is conservative, finding the potential function f so that VJ-7, and using to calculate the work done by 7.

Q: Q6: Find the outward flux of the vector field F=(x²y+e'sin(y))i+ (x²+e'cos (y)) j through the right…

A: Given vector field is F=  x2y + ex siny  i + x2 + ex cosy j Curve r2=cos2θ

Q: Find work done by the force field f = (XY, 2, 42) when a Particle moves along the straight line from…

A: The force field is given as,find work done by the force field F when a particle moves along the…

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: Given the vector field A = (x²+y²) ³/4 (x +yy), → 1) Calculate the line integral of A from the…

A: Q-1The vector fieldA→=1(x2+y2)3/4(xx^+yy^)The line integral from the point origin to (0,1,0)(I) Let…

Q: 5.- Determine the tangential and normal components of the acceleration for the vector function:…

A: Step 1:Step 2:

Q: What is the work done by a force field F (x, y) := 2x to move a particle in a straight line from (0,…

A:

Q: Sketch a direction field for the equation y'= 2y(1-y) by hand. Then use that and sketch a few…

A:

Q: ections 17.2, 17.3) Find the work done by F(x, y) = −2yî – 2xĵ in moving a particle along a line…

A:

Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

A:

Q: b) Show the force field (x, y, z) = (x²y + In(yz)) i+ + y cos(2z) ) j+ y? sin(2z) 3 F k is a…

A:

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

A:

Q: Find the work done by the force field F(x, y) = 2xy³i+ 4x²y² in moving a particle counterclockwise…

A: The work done of a force F→ along a curve r→ is defined by ∫CF→⋅dr→.Since curve is closed in…

Q: 5. Compute the directional derivative and gradient of f(x, y, z) = 4x – y²e3xz at (2, – 1, 0) in the…

A: Gradient of vector function For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is […

Q: 1-2 Find the domain of the vector function. 1. r(t) = (10(1 In(t + 1), t - 2:21

A:

Q: F - () (3x²y²z and F = 2r³yz Q.)11.1 Be (a) Explain why vector fields are conservative. (b)…

A:

Q: (2x+yy), (x²+y²)3/4 → 1) Calculate the line integral of A from the origin of the coordinate system…

A:

Q: (Section 17.2) Find the work done by vector field F(x, y, z) = in moving a particle along curve C:…

A:

Q: Find r'(t), r(t,), and r'(t,) for the given value of to- r(t) = (5 + t)i + t°j, to = 1 r'(t) = r(t,)…

A: To find r'(t) and to sketch the curve represented by a vector-valued function and sketch the…

Q: 64. Let f(t) be a differentiable scalar function and r(t) be a differentiable vector function. Prove…

A: Solutions:- consider ddtft rt=ddtf r  by definition of derivative ddtf. r=limh→0fx+h rt+h-ftrth…

Q: (iv) Find the work done by the force field F(x, y) = x²i+ yeªj on a particle that moves along the…

A:

Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

A:

Q: Suppose C is the curve from (0, 0) to (2, 0) to (2, 3) to (0, 3) to (0, 0). Find the work done by…

A:

Q: Consider the vector field v(z) = i+ i+4k . a) Calculate fu• dr , where l' is the straight line from…

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: A conservative vector field is given as F = 6xe'i + (3x²e" –10yz')j-15y²z°k. Find the potential…

A:

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

A:

Q: 2. (a) Prove that the function f(x, y) = xy is differentiable everywhere in its do- %3D x² + y?…

A: TO solve the question, we use the following facts (a) A functions is differentiable at a point if…

Q: Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out…

A:

Q: Find a potential function for the vector field .F(x,y)=

A: The vector field is