2. Verify that the vector field F(1, y, 2) = sec? y+ -32 2.r tan y + e csc r, 3e -32 cot x + sec z tan z is conservative by finding all of its potential functions.

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: f is a potential function for the vector field F = (2x - 2yz, 3y2 - xz, -2xy) so what is the value…

A:

Q: Find the directional derative of f at the point P0(1,1) in the direction of the vector A = 3i - 2j…

A: Direction derivatives at (1,1) is given in direction of A = 3i - 2j.

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: Find the curl of the vector field F = <yx³, xz³, zy² curl F = i + k + V

A: For the given field F=yx5, xz3, zy2, we need to calculate the curl. This can be evaluated as…

Q: Sketch the vector field F(x, y)=2i-j and calculate the line integral of along the line segment from…

A:

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: A solid material has thermal conductivity K in kilowatts per meter-kelvin and temperature given at…

A: Since the surface is whole sphere, that is S is closed so we can apply Gauss Divergence Theorem.

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: A Particle moves 2 X half way around the circle y² = 4 oriented in the counter-clockwise direction…

A: Given force field: and the path of the particle moving half way around the circle  in the…

Q: Sketch (a) the level surfaces of the scalar point function f(r) = ze; (b) the field lines of the…

A: Given Information:a) Scalar point function: f(r)=ze−xyb) Vector point function: F→(r)=(−y,x,1)To…

Q: Vector Field: F(x,y.z) = (-y, 2rz., x²) and Parametric Curve: r(t) = (21, 31, r> Use the parametric…

A:

Q: The acceleration of a particle at any time >=0 is given by: dr a = == (25cos2t)i + (16sen2t)j +…

A:

Q: Q1:- Find the domain of the following vector fumctions:- (a) f(t) = (cos nt)i - Ln(t)j + Vt-2k (b)…

A:

Q: 10) Use Green's Theorem to find the work done by the force field F(r, y)% = -ry i+yj in moving a…

A: Given force field  Fx,y=-x2yi+yj The particle follows starts from 1,0 moves along the circle x2+y2=1…

Q: 1.Solve the following polynomial equations.  a)  2X3+1=x2+2X

A:

Q: Calculate the work expended when a particle is moved from 0 = (0,0) to Q = (1, 1) along the segments…

A:

Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: Find the potential function for the vector field given as 2 F(x.y.?) = Oa. $(x, y, z) =x*y + x²2?…

A: Answer:   The correct option is B.

Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

A:

Q: Consider the vector field F(2. v) = (--2) i + (8ry° tan ' y) j. i + (8ry² – tan ' y) j. a) Is F…

A: Consider the vector field

Q: Find the outward flux of F = (4x +25y*,0,) 10z through the surface 25 4 9

A: Solution:-

Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: FTTT 10 5 10- -5- -10- X TTTTI 1C d.

A: We draw the sketch of vector field with the help of direction and length of vectors .

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

A: Solution

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

A:

Q: A rental truck costs $45.45 for a day plus 94¢ per mile. (a) If x is the number of miles driven,…

A: Given that, a rental truck costs $45.45 for a day plus 94c per mile.

Q: 2 + v - , 2+z+ 11. 0. di

A:

Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

A:

Q: 2. Let x'= [5, 1, 3] and y' =[-1, 3, 1]. (a) Find the inner product, y'x. (b) Find x- - 2y. (c) Find…

A:

Q: 3. (a) Given the vector valued function r(t) = 4 cos zti + 4 sin atj + tk. Find the position vector,…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 19. Find potential function for = (3xy, æ³)

A:

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

A: The vector field is

Q: dy Draw the direction field for = y ln(x+y) using MATHEMATICA! dx

A: Solution: The graph of the given slope. dydx = xln(x + y)  Shown below.