Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at (2, –1) in the direction of u.

Q: Prove that if u is the vector function with the constant value C, then du/dt = 0.

A:

Q: Find the point on the graph of z = 3x2 + 2y at which vector (24, 8, 2) is normal to the tangent…

A:

Q: Find the directional derivative of f at point p in the direction of vector u. Where z - x f(x,y,z) =…

A:

Q: Let A(5, -1, -3) and B(1, 3, 2) be two points in R. The directional derivative of f(x, y, z) = xy…

A:

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 gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: Let g(x, y) = e*^2 -vy (a) Find the directional derivative of g at (1, 1) in the direction of the…

A:

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: 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: find the velocity and acceleration vectors in terms ofur and uθ .1. r =θ and dθ/dt = 2

A: Given, r=θ and dθdt=2   Find Velocity and acceleration vectors in terms of ur and uθ:

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 gradient vector field of f(x, y, z) = 9x² + 8y* + 6z3

A:

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

A:

Q: Find the gradient vector field of f(x,y) = x2 + y2 and sketch it.

A: Solution

Q: Find the gradient vector field of f(x, y) ,3

A: Given,          The gradient vector field of fx,y=x6y3.

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: 3. Find a vector function that represents the curve of intersection of the paraboloid z =. and the…

A: To find the vector function that represents the curve of intersection of the paraboloid z=x2+y2, and…

Q: Compute the directional derivative of the following function at the given point P in the direction…

A: NOTE: Refresh your page if you can't see any equations. . the given direction is  find the unit…

Q: determine where the given vector-valued functions are continuous. V(1) = (Vi-I ,,1 ). V(t): t-1

A:

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: -2 -1

A:

Q: 2. Find the equation of the normal line and the tangent to the parametric surface defined by the…

A:

Q: Find the point on the graph of z = 3x2 + y at which vector n = (24, 2, –1) is normal to the tangent…

A:

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

A:

Q: Calculate the directional derivatives of functions Inx f (x,y) = x²+ y? in the direction of the…

A:

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: Differentiate the vector-valued function r(t)=⟨sin(t2),4t2−t⟩.

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Q: The position vector of a particle in the xy-plane is given by for all t > 0. The acceleration…

A: position vector of a particle in the xy-plane is given by < t^2+1, ln(2t+3) > for all t>=0

Q: Why is r(t) = ⟨ƒ(t), g(t), h(t)⟩ called a vector-valued function?

A: Given r(t) = ⟨ƒ(t), g(t), h(t)⟩. We need to give reason why r(t) is called vector-valued function.

Q: (b) Identify the unit vector ū pointing in the direction of maximum increase of the function f(x, y)…

A:

Q: Let g(x, y) = e*^2 -vy (a) Find the directional derivative of g at (1, 1) in the direction of the…

A:

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

A: Given, the vector function      r(t)=ta×(b+tc),where       a=4,-1, 5, b=-3,-3, -1, and  c=1, 2, 2,…

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: Let f(x,y)=y2 +sin(y+T)+x +cos(xe). At the point (TT,0) compute the unit vector in the direction of…

A: We have to find the unit vector in the direction of the maximum increase of the function f. This…

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 6t – t3, In(t))

A: Solution-  Given vector function  r(t) = (e-t, 6t-t3, ln (t)) We have to differentiate these…

Q: (b) Identify the unit vector u pointing in the direction of maximum increase of the function f(x, y)…

A: Find your answer below

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

A:

Q: For a scalar function f(x, y, z) = x? + 3y2 + 2z?, the gradient at the point P(1, 2, - 1) is

A:

Q: Find the derivative, r'(t), of the vector function. r(t) = (e-t, 4t - t, In(t) r'(t)

A:

Q: The directional derivative of f(x, y, z) = x? + y? + 4xz at Po(1,-2,2) in the direction of the…

A:

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: Suppose a vector function F(x, y) = 3xi + 2xyj + y ln zk moves along a path C where x = t2, y = t +…

A: The formula to find the work done by the vector function helps to find the required work done. The…

Q: Let F(x, y, z) = 5x² + 2y2 + 522. For which unit vector 0 will the directional derivative DoF at (2,…

A:

Q: The unit tangent vector of the function ⟨2t+1,(3t+1)^2,(2t+1)^3⟩ at the point with parameter value…

A: Topic - vectors Option d

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: dA If A (u)is a differentiable vector function of u and||A (u) || = 1, prove that is perpendicular…

A:

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

A:

Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

A:

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.