Let A(5, -1, -3) and B(1, 3, 2) be two points in R. The directional derivative of f(x, y, z) = xy +11yz +7zx at the point A in the direction of the vector AB is

Q: 3. Let f(x, y) = x² – y². Find a unit vector i for which D7f(3, 4) Dif (3,4) is the directional…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where а 3 (—3, —4, — 2), b — (—2, —5,…

A: Topic:- vector and it's derivatives

Q: Find the directional derivative of the function at the given point in the direction of vector v.…

A: the vector field is  g(x,y,z)=(x+4y+3z)32  point (2,1,1) to find the directional derivative in the…

Q: Find the derivative of the vector function r(t)=ta×(b+tc), where a=⟨3,−2,−3⟩, b=⟨1,3,−2⟩, and…

A: To find the derivative of the vector function, rt=ta×b+tcWhere, a=3, -2, -3, b=1, 3, -2, and, c=-2,…

Q: Consider the function  f(x,y,z) = sqrt(xyz)   what is the gradient of F?   Determine the…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Answer is mentioned below

Q: Find the directional derivative of f(r, y, z) = yr + z* at the point (2, 3, 1) in the direction of a…

A: Directional Derivative of a Function of Three Variables =>Directional derivative of  f ( x , y ,…

Q: Determine the directional derivative of the function f (x, y, z) = x2 + xy + y + z2 in point P = (1;…

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Q: Let f(x,y,z) = x2 y−xy2+z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the maximum…

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Q: (d) Find a vector function that represents the curve of intersection of the two surfaces: the xy…

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Q: Suppose given a function f(x, y, 2) of three variables, and a point (o, y0, 20) €R. Explain in your…

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Q: Let f (x, y) = x 4y-2 and P = (2, 1). Find the unit vector that points in the direction of maximum…

A: Concept: The Unit vector is a quantity which has a magnitude as 1and as well as direction, it is…

Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: Find the derivative of the vector function r(t)=ta×(b+tc) where a=⟨−4,−3,5⟩ b=⟨−1,2,5⟩ and…

A: Solved below

Q: If Ū is a unit vector and Di f(x, y) = 0 for all points (x, y) then f is a constant function..

A: We have to determine whether the following statement is true or false : If U→ is a unit vector  and…

Q: Find the directional derivative Duf(P) of f(x, y, z) = x²y?z²at the point P(1, 2, 3) in the…

A: We have to find the directional derivative of f(x,y,z).

Q: (a) Find the directional derivative of the function f(x, y) = 4.xy – x2 – y? in the direction of…

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Q: Find the directional derivative D, f(2, –3, -3) for the function f(x, y, z) = ry + yz + zx in the…

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Q: Find the derivative of the vector function r(t) = ta x (b+tc), where (5,-4, 1), b = {(-4, –3,1), and…

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Q: Find a unit vector in the direction in which f (x, y, z) = 3x³z² + 3y°z + 24z – 4 increases most…

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Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 +y =…

A: Given Data: The equation of the curve is: x2+y2=4 ......1 The equation of the plane is: x+z=3…

Q: 1. Let f(x, y) = r³ + x?y + xy? + 2y³. a) Compute the gradient vector Vf(-1,2). b) Let i = (-3, 4).…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: Exercise III Let (a) o = x²y +xż and (b) ó = x² + y² + z?. Then, respectively attempt to find the…

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Q: Suppose that ∇ƒ(x, y, z) is always parallel to the position vector x i + y j + z k. Show that ƒ(0,…

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Q: Let f(x, y, z) = x2y− xy2 + z3, P(1,1,2), u is the vector from P to Q(1, −2, −2). Determine the…

A: The objective is to determine the maximum and minimum directional derivative at P and give a vector…

Q: b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1,…

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Q: Find the directional derivative of f(x,y,z)=xe +ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines, I can answer only one question. To know rest please re upload particular…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: The objective is to find the directional derivative of the given function h(r,s,t) along the point…

Q: Find the directional deriu atrue Du f(-3,-1,3) for the function f (xiy,z) =xy + yz +Z X in the…

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Q: Find the directional derivative of f(x,y,z)=xeY+ye² at (0,0,0) in the direction of the vector…

A: As per our guidelines I am solving only first question please resubmit other question.  To find…

Q: The directional derivative of the function f(x, y, z) = x³y4 – 3z2 at the point (1, 1,1) in the…

A: we have to find the directional derivative

Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: The position of a particle moving in the xy-plane is given by the vector (4t, y(2t)), where y is a…

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Q: h (r, s, t) = ln (3r + 6s + 9t), (1, 1, 1), v = 4i+ 12j + 6k

A: We have hr,s,t=ln3r+6s+9t at 1,1,1 in the direction of v=4i+12j+6k

Q: Find the directional derivative of the function at the given point in the direction of the vector…

A: This is a problem of Vector Calculus.

Q: Find the directional derivative of the function at the given point in the direction of the vector v:…

A: I am going to solve the given problem by using some simple calculus to get the required result.…

Q: Find a unit vector that is normal to the level curve of the function f(x, y) = 5x + 6y at the point…

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Q: Let f (x,y,z) = xye² + yze*. From point (1,0,1), which unit vector points in the direction in which…

A: Consider the given information. fx,y,z=xyez+yzex The point is 1,0,1. The direction in which f…

Q: Find a vector that gives the direction of maximum rate of increase for the e2y cosx at (n/4,0).…

A: Consider a function . Then the maximum rate of change of this function occurs at the direction of…

Q: a) Find the directional derivative f (x, y, z) = x In(y+z) at point P (2, e, e) in the direction of…

A: We have to find directional derivative of vector f in the direction of vector v:

Q: Let h(r,y) = r'e. Find its linearization at the point (1,0) and use this to approximate f(2,0). %3D

A: Given function is h(x,y)=x2ey we have to find linearization at point (1,0). then to approximate…

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: 2. Find the directional derivative of f(x,y, z) = x²y + yz² at P(1,–1,3) in the direction of vector…

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Q: Suppose that in a certain region of space the electric potential V is given by V (x, y, z) = 8x ^…

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Q: Let f(x, y, z) = x² – y? + 2z. Compute the rate of change of f in the direction of the vector (v2,…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: Finding the directional derivative of the given function

Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

A: To find the directional derivative of the function at a point in the direction of the given vector,…

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

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Q: Find the derivative of the vector function r(t) = ta x (b + tc), where a = (2,-2, 5), b (2,-5, 3),…

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Q: Let f(x, y, z) = x+y+z. What is the directional derivative of f in the direction of the unit vector…

A: The function is given by fx,y,z = x+y+z Unit vector is given by u = a,b,c To evaluate : The…