2. Find the directional drevative of f(x, y,z) xsinyz at the point (1,3,0) in the direction of i =i+ 2j + 2k.

Q: If the electric potential at a point (x, y) in the xy-plane is V(x, y), then the electric intensity…

A:

Q: 1. Find the work done by the force F(x, y, z) = (xz, z² – x, y ), along C, the curve defined by x =…

A:

Q: Find the directional drevative of f(x, y, z)=xsinyz at the point (1,3,0) in the direction of v = i +…

A: we have to find the directional derivative of f(x,y,z)=xsin(yz) at the point (1,3,0) in the…

Q: 1) For f(x,y, z) = x² – (1 – y)² + z². Find directional derivative of f at P(1,1,1) in the direction…

A: As per our guidelines we are supposed to answer only one question.Since you have asked multiple…

Q: Use Green's theorem to evaluate Sc(y² + x³) dx +xª dy where C is the perimeter of the square [0, 1]…

A:

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

A:

Q: Find the work done by the force F (r, y) = yxi– (x – y) j over the straight line from (1, 1) to…

A:

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, yo, 20) is given by the…

A: Given: Surface f(x, y, z)=c and a point x0, y0, z0 To show: Equation of tangent line to f(x, y, z)=c…

Q: Evaluate the line integral f. (2x – 4xy)dx + 3xy – 2x³y)dy over the straight path L joining point…

A:

Q: Consider the function f(x, y) = ax – 2y + 1 where a is a positive number. S SR ax 2y + 1 dA = 45,…

A: A double integral involves the integral with respect to the product of any of two variables in x,y,…

Q: Compute the directional deri vative of the function f(z,y, 2) = zy² + y²9+°% at the point P(4, –2,…

A: Given function is fx,y,z=xy2+y2z3+z3x

Q: What is the directional derivative of the function f(x, y, z) = 2xy + z² at the point (1, –1,3) in…

A: The Directional Derivative: Let the function f(x, y) be the height of a mountain range at each point…

Q: Study the analytically of w = L_r(z) at the points z = 0, z = v2,z = -2i

A:

Q: 2. Use the limit definition to find the directional derivative of the given function f at the given…

A:

Q: 2. Find the directional drevative of f(x, y,z) xsinyz at the point (1,3,0) in the direction of v = i…

A:

Q: Find the directional derivative, Dvf , of (*) f(x, y, z) = 4x tan 1 at the point P = (1, 1, 1) in…

A: To find the directional derivative of f(x,y,z) at P=(1,1,1) and the Direction, v=(1,2,2).

Q: 35. f(x, y) = x+2y2 -x; R is the disk x2+ y? < 4.

A:

Q: Find the directional derivative of the function z(x, y) = In(x² + y²) at the point M(xo, Yo), in the…

A: The directional derivative of function z=fx,y in the direction vector u is calculated by the formula…

Q: For f(x,y, z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: The directional derivative of a function f  in the direction of the vector u is given by…

Q: (B) Find the potential function V = V(r, y) such that %3D + yi+ + r)j = V¥ 1+ x2 + y? 1+ x? + y? and…

A: We have to find the potential function ψ=ψx,y such that x1+x2+y2+yi+y1+x2+y2+xj=∇ψ and also evaluate…

Q: find the outward flux of F across the boundary of D.  F = 2xyi + 2yzj + 2xzk D: The cube cut from…

A:

Q: Given that F = (2x + y2)i + (3y – 4x)j. Verify Green's theorem for F.dr around the triangle formed…

A:

Q: Find the directional deriyative of f(x, y)=y In x at the point (1, 4) in the direction of V=-3i +…

A:

Q: 1. Evaluate the line integral f(z, y) ds where f(x, y) = Vx+ 2y and C is the straight-line segment…

A:

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

A:

Q: Find F.dS if F (x, y, z) = 2xi+2yj+2zk and S is t he part of the paraboloid z = 8-x²–-y? lying above…

A:

Q: Consider F and C below. F(x, y, z) = (y²z + 2XZ² ) Î + (2xyz)j + (xy² + 2x² Z) K₂ C² X=√E, y = t +…

A:

Q: Compute the directional derivative of f(r. y) = = at the point (1, 1) in a irection normmal to the…

A:

Q: Find the directional derivative of f(x, y, z) = x²y−yz³ + z at the point (1,−2, 0) in the direction…

A: Solution:f(x, y, z) = x²y−yz³ + zat the point (1,−2, 0) in the direction of the vector a = 2i +…

Q: Q2) Find the directional derivative of F(x,y,z)= sin(yz)+In(x³) at the point(1,1,7) in the direction…

A: This question is related to vectors, we will use gradient of function to solve this.

Q: Find the work done by the force F = xy i + ( y - x)j over the straight line from (1, 1) to (2, 3).

A:

Q: Find the Directional Derivatives of f (x, y) = ey at (2, 3) in the direction v = 3i – 4j

A:

Q: 8. Let f (x, Y, z) = ln (x² + y² – 1) + y + 6z. In what direction ī is f(x,y, z) increasing most…

A:

Q: In Exercises 11-14. find the directional derivative of f at P in the direction of a. 11. fx. y, 2)…

A:

Q: Consider z = Ax + By + D be the tangent plane to f(x, y) = 2x² + 5y³ + 9xy + 9x + 3y at (6,9).What…

A:

Q: 1. (a) Let /(r,y)- cos(z + 2y). Compte the directional derivative Da/(r.y), where u- (b) Compute ff,…

A: Given that, In part (a), f(x, y) = cos(x+2y) u=(x,y)=-12,12 We have to find the directional…

Q: Compute the directional derivative of f at the given point in the direction of the indicated vector.…

A:

Q: 2. (a) Let z ry, r =r cost and y=r sin t. Compute by using the chain rule and express your answer in…

A:

Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: Evaluate the fuctions at the given values of the independent variablels.   u= f (w, x, y, z)=…

A:

Q: 5. Show that the equation of the tangent plane to f(r, y, z) = c at (ro, Yo: 20) is given by the…

A: This is the question from vectors.

Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

A:

Q: Find the work done by the force F= xyi + (y - x)j over the straight line from (-1,- 2) to (2,1).

A:

Q: (b) Find the directional derivative of the function f(x,y,z) = xy sin z at the point (1,2, %3D T2)…

A: Solution:

Q: Find the directional derivate of f (x, y) = tan (3xy) at the point (1,2) in the direction of 3i - j.

A:

Q: For f(x,y,z) = x² – (1 – y)² + z?. Find directional derivative of f at P(1,1,1) in the direction of…

A: Since there are two questions posted, we will answer the first question posted (1). If you want the…

Q: 9. Find the directional derivative of f(x , y , z) = 3x° +y° +z° - 9x + 9y – 9z + 4 at the point 9.…

A:

Q: (b) Use the corresponding formula to evaluate the line integral F. ds where F(x, y, z) = (xz, -yz,…

A:

Q: 9. Evaluate the line integral ſo F · dr, where F(x, y) = (ry, 3y?), and C is is given by the vector…

A: We have to integrate F • dr over the curve C given by the vector function r(t) = ( t4, t3 ) for t in…

Q: find the general solution of the dipperential ation given below. y+ 2xy -xe-r?

A: