speed of a particle with position function r(t)=⟨8cost,−6t,8sint⟩r(t)=⟨8cos⁡t,−6t,8sin⁡t⟩ ⟨v(t)=⟨ , ,  ⟩ ⟨a(t)=⟨ , ,  ⟩⟩ |v(t)|=

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: Find ∇f(x, y, z) for the function f(x, y, z) = x2 + y2 − 4z and find the direction of maximum…

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Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: 5. Find the gradient of the curve i) y = 3e-2x – 1 at the point where x =. ii) y = xv2x - 3 at the…

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Q: 3. Find the gradient of the function and the maximum value of the directional derivative at the…

A: As per our guidelines,we are supposed to answer only one asked question.So kindly repost other…

Q: let f(x,y,z)=ax3y + by2e1-z+cze1+z be a function . Find a, b, c, so that the maximum value of the…

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) : x2 + y2 + z? (7,…

A: Formula for the directional derivative of the function f(x,y,z) is: ∇f = fxi +fyj +fzk Where…

Q: Find the maximum rate of change of the function f(x, y, z) = xy + yz - xz at the point P,(1, -3, 4).

A: As per our guidelines we are supposed to answer only one question.

Q: Find the gradient of the function f(x.y) = /2x+ 3y at the point (- 1,2). Then sketch the gradient…

A: Solve the following

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

A: We have given function, we have to find directional derivative.

Q: Tangent to the curve z2 = 2xy + x2 , z = 3 , at the point ( 1, 4, 3) %3|

A: For a surface of the form: f(x, y, z)=0, the equation of the tangent at x0, y0, z0 is defined as…

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

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Q: Q4:- Find the derivative of the function at Po in the direction of the vector AC. f(x, y, z) = x² +…

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Q: Find the gradient of the function at the given point. In(x² – y) – 8, (3, 8) Vz(3, 8) =

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Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: Since, you have posted multiple question. I am answering first one. Please post again with specific…

Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) 3 x2 + y2 + z2 (7,…

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Q: Find the gradient of the function and the maximum value of the directional derivative at the…

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: What does it mean for a function ƒ(x, y) to be differentiable? What does the Increment Theorem say…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z2 (4,…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: Gradient problem....

Q: F(1), p(y) - y - 1, F(Y) - F(y - 1), y - 2, 3, ...

A: Suppose that Y is random variable that takes on only integer value 1,2,.. and has distribution…

Q: Find the direction of maximum decrease of the function f(x, y, z) =exyz at the point P(1,1,1) and…

A: Given function is

Q: Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It…

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Q: Find the gradient of the function at the given point. g(x, y) = 5xev/x, (8, 0)

A: Follow the procedure given below.

Q: a) Compute the directional derivative of the function shown below at the point (1, 0, -2) in the…

A: The given scalar field is - f(x,y,z)=(x^2)z+(y^3)(z^2)-xyz

Q: Evaluate the directional derivative of the function f=x^2-y^2+2z^2 at the point A (1,2,3) in the…

A: Point A(1,2,3) and Point B(5,0,4) ⇒AB→=5-1i^+0-2j^+4-3k^=4i^-2j^+k^ Now we have to find the…

Q: The productivity of a certain country with the utilization of x units of labor and y units of…

A: It is given that,  f(x,y)=100x0.72y0.28

Q: w = 3x² – 5y² + 2z², (1,1, –2)

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx² + y2 + z² (2,…

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Q: Consider a function of 3 variables h (x, y, z2) = -3 (2+ Calculate the value of its third order…

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Q: Find the gradient of the function at the given point. Function Point (3, 7, 2) f(x, y, z)=√√√√x² +…

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Q: Find the gradient of the function at the given point. Function Point x + 2y y + 1 f(x, y) = (1, 2)…

A: We have to find

Q: Find the gradient of the function at the given point. w = x tan(y + z), (10, 5, -2) Vw(10, 5, -2) =

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Q: 4. Find the gradient of the function f(x, y) = cos(x² + y²) at the point (3,-4). 5. Find the…

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (9, 5, -1) Vw(9, 5, -1) =

A: Gradient of function is ∇w=i^∂w∂x+j^∂w∂y+k^∂w∂z where i^, j^, k^ are unit vectors along x, y, z axis…

Q: Find the directional derivative of the function at the point P in the direction of the point . f(x,…

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Q: 3) Find the directional derivative of f(x, y) = xex-yx² at (-2,1) in the direction v=i-j B) g(x,y) =…

A: The directional derivative of the given function at p in the direction of u→ is  Duf(P)=∇f(P)·u^ Let…

Q: Find the gradient of the function at the given point. Function Point F(x, y, z) = Vx2 + y² +. (5, 4,…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y2 + 6,    (3, 1)

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Q: Tangent to the curve z2 2xy + x² , z = 3 , at the point ( 1, 4 , 3 )

A: Consider the curve, z2=2xy+x2 ⇒x2+2xy-z2=0

Q: 6. Find the directional derivative of the function f (x, y, z) = x²z – xyz³ + xyz + y – 1 + z from…

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Q: Find the gradient of the function at the given point. Function Point f(x, у, 2) + y2 + z2 (3, 7, 2)…

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Q: Find and sketch the domain of the function. f(x, y, z) = ln(64 − 4x2 − 16y2 − z2)

A: Given function is      f(x,y,z) = ln(64-4x2-16y2-z2) We have to find the domain of this function.

Q: Find the gradient of the function at the given point. w = x tan(y + z), (5, 8, -1) Vw(5, 8, -1) =

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Q: Tangent to the curve z2 = 2xy + x² , z = 3 , at the point ( 1, 4 , 3

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Q: Find the gradient of the function at the given point. w = x tan(y + z), (12, 7, -2) Vw(12, 7, -2) =

A: Gradient of function wx, y, z=xtany+z at point 12, 7, -2

Q: Find the linearization of f(x,y) at the indicated point (X0.Yo)- f(x,y) = /x + 2y; (1,6) L(x,y) =

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