Q19:- Find the magnitude of the maximum and minimum directional derivatives of the function w = e2xy4 sin² z, at the point Po(0,1,) and the unit vector of each one.

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 velocity and acceleration vectors in terms ofur and uθ . r = 1/θ and dθ/dt = t2

A: Given Data The position vector is r=1/θ. The change in angle vector is dθ/dt=t2=2t.   Integrate the…

Q: Find the directional derivative at (1,0) if Vƒ(1,0) = in the direction of the unit vector u = i?…

A: Given : ∇f(1,0)=<-4,3>   To Find: directional derivative at (1,0) in the direction of the unit…

Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(8t), sec(3t), r'(t) =

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Q: Find the derivative, r'(t), of the vector function. r(t) = tan(8t), sec(4t),

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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: Represent the plane curve by a vector-valued function. x- + y2 = 4 r(t) = 2 cos ti +2 sin tj

A: x2 + y2 = 4 x2 + y2 = 22 = r2 Therefore, r = 2

Q: For the function f(x,y)=x^3−2x^2y−y^2−y, which vector is normal to the level curve at the point…

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Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(: OS…

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Q: Find the derivative, r'(t), of the vector function. r(t) = ( tan(2t), sec(5t),

A: We have to find the derivative of the given vector function  r(t)=< tan(2t) ,sec(5t) , 1/t^3>…

Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

A: For the solution follow the next steps.

Q: A point, p, is moving with acceleration 6t j -k at time t. If at t 1, the coordinates of P are (1,…

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Q: Q2. A point is moving along a curve whose position vector is Find : the acceleration components at /…

A: Consider the given position vector

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: Let f (x, y) = x² + 4xy². Say the directional derivative Du(1,1) with u is the unit vector that…

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Q: c) Find the directional derivative of f(x,y) = 10 – 3x2 + at P(2,–3) in the direction of the vector…

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Q: Find a vector equation for the tangent line to the curve 7(t) = (5 cos(6t)) i + (5 sin(6t)) j+…

A: Given the vector function, r(t), we call r′(t) the tangent vector provided it exists and provided…

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

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Q: Determine a direction derived from the point P and in the direction of the versor vector → informed…

A: Given:  Let f be a differentiable function at the point (a, b). Then f has a directional derivative…

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t), sin(3t), cos(3t))…

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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: At which point P of the curve defined vectorially with r (t) = (21, 4t + 1, t) is the tangent vector…

A: The general form of the parametric equation of the curve in three dimensional space is given by…

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: V3 t², a cost + at sin t) 2 r(t) = (a sint – at cos t,

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Q: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x -…

A: Given function is w=x2-3xy-y2+2xz2+6yz

Q: B-For the surface z² = x² + y² find the directional derivative at the point (√2, √2,-2) in the…

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Q: Given the following vector problem, SOLVE for the directional derivative of f = 2xz2 – 3xy – 4x at…

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Q: Q3) For the vector function f(t) = [2e", te?, 3 te? 1, Determine the point of %3D tangency and the…

A: We have to find the point of tangency and unit tangent vector at t=2.

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

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Q: A curve is given by the parametrization r(t)= [²,-t, ť ]. If the tangent vector to this curve at a…

A: The given curve is,  ,

Q: The largest value of the constant b such that the vector-valued function F(t) =< cos 21It, sin (t-…

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Q: Find a vector equation of the line tangent to the graph of r(f) at the point Po on the curve. r(1) =…

A: Find the derivative of the function r(t) to find the equation tangent to the graph of the function.…

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: 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: Which of the following is the directional derivative of f(r, y) = z'y at the point (-1,-1) in the…

A: The directional derivative formula is given by Duf(x,y)=∇f(x,y)⋅u, where u is the unit vector and…

Q: Q18:- Find the magnitude of the maximum and minimum directional derivatives of the function w = x3 –…

A: Directional derivative are given by gradient of function

Q: Q1. Find the directional derivative of = x²z + 2xy² + yz2 at (1, 2,-1) in the direction of vector…

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Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

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Q: f(x, y) = e2² –3y°, u = (0, 1).

A: The directional derivative of fx, y in the direction of u=a, b is as follows. Dufx, y=fxx, ya+fyx,…

Q: Which of the following is the directional derivative of f(r, y) at the point (0,0) in the direction…

A: Formula to find the directional derivatives helps to find the required directional derivative in the…

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

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

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Q: c) Find the directional derivative of f (x, y) = 10 – 3x? + at P(2, –3) in the direction of the…

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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: (iii) Find a vector equation for the tangent line to the curve of intersection of the cylinder a² +…

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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: p1. Find the directional derivative of o = x²z+ 2xy² + yz? at (1, 2,-1) in the direction of vector…

A: on using gradient we get

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

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