b. Find the directional derivative of the function f(r, y, z) = re" + ye + ze" at the point (1, 1, 1) in the direction of the vector v = 8i – 6k.

Q: Find the directional derivative of f(x,y, z) = xy + yz + zx at the point P(1, 1, 1) in the direction…

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

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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…

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Q: 10) Find a unit vector in the direction that f (x, y, z)= 2x² +6xy² – xz' increases most rapidly at…

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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: find a vector normal to the plane with the given equation. x − z = 0

A: Given: Plane: x-z=0 To Find: A vector normal to the given plane

Q: find the vector function r(t) given r'(t) and the initial condition

A: Solution: The objective is to find the vector function r(t)

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

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Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at 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: Find the directional derivative of f(x,y,z)=xeY+ye² at (0,0,0) in the direction of the vector…

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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 the function f (x, y) = x² + xy at the point P, (1, 2) in the…

A: Topic:- directional derivatives

Q: Find a vector n normal to the plane with the equation 5x - 5y – z = 10. n = (5,

A: Given equation of plane is 5x-5y-z=-10.want to find:Normal vector n to given plane.

Q: Sketch the curve represented by the vector-valued function                              r(t) = (t +…

A: Given: The vector-valued function  r(t) = (t + 1)i + (3t − 1)j + 2tk and it gives the orientation of…

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

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Q: Find the vector equation of the plane tangent to the surface z = x^3 - y^3 at the point (0,1,-1)

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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: Find a vector n normal to the plane with the equation – (x + y+ 52) = –4. n = (-1,

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

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Q: A particle moves in the x – y plane with velocity v=(1-t)î +(4– 2t + t² )j where t is the time and i…

A: As per our guidelines we are supposed to answer only first three subparts of question at a time.…

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…

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Q: 2. Find the directional derivative of the function f(x,y,z) = xy? – 4x?y + z² at (1, -1, 2) in the…

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

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Q: The vector equation for the curve of intersection of the surfaces x = y² and z = y in terms of the…

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

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Q: Compute the directional derivatives of the following functions along unit vectors at the indicated…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

A: To find a vector tangent to the curve of intersection of two cylinders        x2+y2=2 and…

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 a vector function that represents the curve of intersection of the paraboloid z=7x^2+5y^2 and…

A:

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

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Q: find the velocity and acceleration vectors in terms ofur and uθ . r = a(1 - cos θ) and dθ/dt = 3

A: Velocity is defined as the rate of displacement. Acceleration is known as the rate of change in…

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: Given that, gu,v=u2e-v,8,0 and v=3i+4j. Find the value of ∂g∂u and ∂g∂v at the point (8,0).…

Q: Compute for the directional derivative of f (x, y, z) = tan (Tx – 21ny)e4y-z at the point (, 0, In…

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Q: Find the directional derivative of o = x2 + 2xyz – yz? at the point (1, 1, 2) in the direction of…

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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: 11. Calculate the directional derivative of the function f(, y, z) = xyz at the point a (-1,0,2) in…

A: See the answer below

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 velocity and acceleration vectors in terms ofur and uθ . r = a(1 + sin t) and θ = 1 - e-t

A: The velocity and acceleration in terms of ur→ and uθ→ are given by: v→=r'ur→+r θ'uθ→a→=r''-r…

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: Calculate the directional derivatives of functions f(x, y)= x? – y? .2 in the direction of the…

A: