(2) Find the work done by F over the curve C in the direction of increasing t. Explain why the sign of your result "makes sense." F(2, y, 2) = zî + æ ĵ + yk C : F(t) = sin(t) î + cos(t) ĵ + tk, t E [0, 27]

Q: Verify Stokes's theorem for F =, where C is the curve C: x² + y² = 4, z = 2

A:

Q: 2: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G(x, y) = x³y² + y² sin…

A:

Q: dr. Let f(z) =z. Find from z-0 to Z-4+2í alongthe curve C given Z=21 to z=2i

A:

Q: Find the work done by F over the curve C in the direction of increasing t,where F =-5 vi +5xi+8z’k…

A:

Q: find the work done by F over the curve in thedirection of increasing t. F = 6z i + y2j + 12x kr(t) =…

A:

Q: F(x,y) = (1+ 2xy?)î+ (2x°y +2y)}

A:

Q: (b)Find the derivative of g in the direction of a= 2i+ curl w where at point (0,-1,1) g = In- 4 + 2…

A: Given, w=cosxyzi+xeyz+1j+xyzk Then, Curl…

Q: Evaluate | f(x,y) ds where Cis the portion of the curve y = In x from the point (1,0) to the point…

A:

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j+ sin(rt) k. %3D…

A:

Q: If w= y(x- mz)i + yz*j + In XZ -1 k and f-w cos (xy-x) x* + m y find at point (0,2.-m): (1) the…

A: Given - If w = yx - mzi + yz2j + lnxz - 1x2 + mk and f = w ·cos-1xy - x2yj To find - At point ( 0,…

Q: et C be a portion of a curve from (2,0) to (2,2). Let F(r, y) = (tan(2?) +2, ) Is F conservative?…

A: In the given question, the concept of integration is applied. Integration Integration is a method of…

Q: 1. Let f(x, y) = -x2 – xy³ + 7. Find an equation for the plane tangent to f at (3, 2).

A:

Q: 1. Find one normal vector of the tangent plane to f(x, y) = cos(x² + y²) at point P(1, 1, cos 2). 2.…

A: 2. The equation of the tangent plane to f(x,y)=sin(x2+y) when x=0, y=π

Q: The tangent line to the curve r(t) =(t°,t“, t³ ) at the point (1, 1, 1) intersects the æy-plane at a…

A:

Q: directional derivative

A:

Q: 2 The tangent plane to the graph of the function ƒ : R² → R defined by f(x, y) = −1+ cos(xy) +…

A:

Q: Show that / F. dr is independent of its path, given that F(x, y, 2) = ( : 2) i+ tan-lr j+ k. 1+ 22 +…

A: Here we will find out the required value.

Q: Show that F. dr is independent of its path, given that F(л, у, 2) — + tan 1+x² 2) i+ tanrj+ k. 1+2²…

A: We will show the required result.

Q: find the work done by F over the curve in thedirection of increasing t. F = z i + x j + y kr(t) =…

A:

Q: Evaluate the line integral f. F. dr where F = (2 sin a,–5 cos y, 10xz) and C is the path given by…

A: We will evaluate the given line integral.

Q: Q4. Let C be a portion of a curve from (2,0) to (2, 2). Let F(r, y) = (tan(2²) + e²", 2.re²y + cos…

A:

Q: Express the curve by an equation in x and y given x(t) = sin(t) and y(t) = 8 + cos² (t). a) O-x² +y…

A:

Q: .: Evaluate [G(x, y)dx, [G(x,y)dy and [G(x, y)ds on the indicated curve C. G (x, y) = x³ y² + y² sin…

A:

Q: 8. (a) Show that F(x, y) = (ye + sin y)i+ (e" + x cos y + 2y)j is conservative and find a function f…

A:

Q: Encontrar la transformada de laplace de la función f(t) = { 2, si 0 2π

A:

Q: Verify Stoke's Theorem for F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1…

A: Given: F =( x²)i +(xz)j + (xyz)k and C is the curve of intersection between z=1 and z² = x² + y².

Q: Evaluate F. dr where F = (x – 3y)i + (y – 2r)j and C is the closed curve in the xy plane, x = 2 cos…

A:

Q: Consider the curve C in RS parameterized by r(t) = sin(2t) î + cos(t) ĵ+t k, con 0 <t < 2n An…

A:

Q: 3. Find the work done by F over the curve in the direction of increasing t. = (2,x, y) = (sin t, cos…

A: Write the vector field F=zi+xj+yk The equation of the curve. rt=sinti+costj+tk Differentiate…

Q: 1. Sketch in the xy - plane the domain of each function : (a) ƒ (x, y) = (Vx – 1+ Vy +1) · In (x² +…

A:

Q: 3. Let the curve C be traced by the vector-valued function R(t) = cos(at) î + at j + sin(at) k. Find…

A:

Q: 1. If F(x, y) = (3+2xy)i + (x² – 3y²)j. Evaluate F. dr, where C is the curve given by r(t) = e'…

A:

Q: 5. Let f(1, y) = re" + cos(ry) and P: (2,0). A. Find the directional derivative of f at P in the…

A: Given information: The function is f(x,y)=xexy+cosxy and P:(2,0) and the vector is v=3i-4j. (a) To…

Q: find the work done by F over the curve in the direction of increasing t. F = 2y i + 3x j + (x + y)k…

A:

Q: B) Evaluate the line integral F-dr, where F (x, y) = x²y³i+ x°y°j and C is the curve r (t) = (t³ –…

A:

Q: 4. Integrate f(x, y, z) = Vx² + y² over the involute curve (cos t + t sin t)i + (sin t – t cos t)j,…

A:

Q: i+ (x-my)j + zx*k and f=w0 0 cos "(yz - y²) xy If w In + m find at point (-m,0,2): (1) the…

A: We are provided with functions: w=lnxy-1y2+mi+zx-myj+zx2kf=w·cos-1yz-y2zk The objectives are at the…

Q: Use Green's Theorem to evaluate / F · dĩ, where F = (VE + 3y, 2x + vũ) C consists of the arc of the…

A:

Q: Find the work done by F over the curve in the direction of increasing t. F=xyi + 8j + 6xk; C: r(t) =…

A:

Q: 3. Let f(x, y) = xy² + x°y². Find an equation for the tangent plane at (x, y) (-1,2). %3D

A:

Q: find the work done by F over the curve in the direction of increasing t F = 6z i + y2 j + 12x k r(t)…

A:

Q: (e) Set x(t) = 2 cos(t), y(t) = 2 sin(t). Draw the parametrized curve (r(t), y(t)) in the ry plane…

A: According to question, fx, y = 3x2 + 5y2e-x2-y2 You have asked particular subpart, so i have to…

Q: find the work done by F over the curve in the direction of increasing t. F = z i + x j + y k r(t) =…

A:

Q: Find the work done by F over the curve C in the direction of increasing t,where F=-5 yi+5xj+8z°k and…

A:

Q: Show that the curve r(t) = ( t3 /4 - 2)i +(4/t-3)j+cos(t-2)k is tangent to the surface x3 + y3 + z3…

A:

Q: how that the function satisfy Laplace equation f(x,y) = In /9xy+3y²

A:

Q: find the work done by F over the curve in the direction of increasing t. F = z i + x j + y k r(t) =…

A:

Q: 3. Find S. F · dr where F(x,y, z) = (3y²e*, 6ye* F(t) = (sin t, ,2-) for 0 <tsn. 1+3) and C is the…

A:

Q: 2. Find the parametrization of the tangent line to the space curve r(t) = (-t3, In(t), e² ) at t =…

A:

Q: Evaluate [xy dx+(x+y)dy along the curve y=x² from (−1,1) to (2,4). [Verify using Mathematica]

A: