Find the velocity and acceleration vectors of the particle whose position at time t seconds is given by s = (t',t",(3t-1)') at the instant that t =1. If distances are measured in meters, what is the speed of the particle at this time?

Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

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Q: Find the tangential and normal components of acceleration for a projectile fired at an angle 0 with…

A: we know that for projectile fired at angle θ with the horizontal tangentialTt and normalNt…

Q: Compute the directional derivative of the function g(x,y) = sin (x(4x – 5y)) at the point P(3, – 3)…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(xy)…

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

Q: 2. Suppose that f (1,2)= 3 and that the directional derivative of fat point (1,2) in the direction…

A: Given that f1,2=3 and the directional derivative of f at point (1,2) in the direction of the vector…

Q: For f(x, y) 5æ sin(ry) at the point (3, 5), the direction in which the maximum rate of change occurs…

A: The objective is to find the direction in which maximum rate of change occurs.

Q: In what direction ữ is f(x, y, z) increasing most rapidly at the point (1, 1, 0)? Give your answer…

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Q: Find the velocity and the position vector of a particle that has the given acceleration and the…

A: The objective is to find the velocity and position vector of the particle.

Q: A body of mass m falls from the rest in a medium offering resistance proportional to the square of…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

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Q: A bee with velocity vector r' (t) starts out at (3, –5, –2) at t = 0 and flies around for 3 seconds.…

A: Let f(x) be a continuous function in the interval a,b . The the fundamental theorem of calculus…

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 3x sin(zy)…

A: The maximum rate of change of a function f(x, y) at (a, b) occurs in the direction ∇f(a, b)  where…

Q: 2. Suppose that f (1,2) = 3 and that the directional derivative of ƒat point (1,2) in the direction…

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Q: At time to, a moving particle has the velocity vector v = 7i and the acceleration vector a = 7i +…

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Q: Find the diectional derivative of the function f (xiy,z)= sin (xy+2) at the point of P(1, al2 x4) a…

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Q: 5. Suppose a particle is moving along a smooth path r(t) with constant speed. If a(t) + 0, show that…

A: Two vectors is perpendicular if their dot product is zero.

Q: Suppose that f (1,2) = 3 and that the directional derivative of f at point (1,2) in the direction of…

A: Given : f1,2=3 and the directional derivative of f at 1,2 in the direction of the vector i+j is…

Q: Find the increase rate of the scalar V at point P from origin to the point P(2,6; 9,8 ; 9,5) where…

A: According to question given that The origin to the point P(2,6 ;9,8 ; 9,5) where V=3, 3xy+ 2, 6xyz

Q: Find a vector equation of the tangent line of f(t) = (cost, sint, t) at the point Po (0, 1,

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Q: Find the directional derivative of the function f(r, y) = 1+5x /j at the point (5, 1) %3D in the…

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Q: Find the directional derivative of f at the point (1,2) in the direction of the vector v = = (1, 3).

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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 +…

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Q: Use the full differential to calculate an approximate modulus value. of the vector (5, 8 ; 3, 1 ; 2,…

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) : 5x sin(xy)…

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Q: Compute for the directional derivative of f (x,y,z) = tan (ax – 2ny)e4y-z at the point (,0, ln 4) in…

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Q: Suppose ƒ is differentiable at (9, 9), ∇ƒ(9, 9) = ⟨3, 1⟩, and w = (1, -1). Compute the directional…

A: Given that ∇ƒ(9, 9) = ⟨3, 1⟩. Note that w = (1, -1) is not a unit vector. Its unit vector along same…

Q: 4. Determine the directional derivatives of $(x, y) = tan"2+3 sin ). at the point (1,1) in the…

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Q: Find the unit vector towards the tangent of the curve y = x at x =1

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Q: A projectile of mass m is launched from an initial position r0 with an initial velocity v0. Find its…

A: Consider the given initial velocity v0 and initial position r0

Q: Find the direction in which the maximum rate of change occurs for the function f(z,9)2zsin(ay) at…

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Q: Find the directional derivative of the function f(x, y) = 2x2y + 6xy at (1, 1) in the direction of a…

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Q: Find the unit vectors that are parallel to the tangent line to the parabola y = x² at the point (5,…

A: Given: y=x2 at the point (5,25)

Q: Suppose that f(I,2) =3 and that the directional derivative of fat point (1,2) in the direction of…

A: Thr given problem is to estimate the value of f(1.1,2.1) with given values f(1,2)=3 and directional…

Q: For f(z, y) is: = 5a sin(xy) at the point (2, 4), the direction in which the maximum rate of change…

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Q: Find the maximum rate of change of f(x, y) Maximum rate of change: = In(x² + y?) at the point (3, 1)…

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Q: Compute the directional derivative of f (x,y)= at the point (1,1) in a direction normal to the…

A: The directinal derivative is given below

Q: 5. Compute the directional derivative and gradient of f(x,y,z) = 4x – y²e3xz at (2. –1.0) in the…

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Q: What is the rate of change of the function f(x,y) = ye^(2cos x) + tan(x+3y) at ( 3π/2 , π/2) in the…

A: Given: fx,y=ye2cosx+tanx+3y To Find: Rate of change of fx,y in the direction of the vector 3,4 at…

Q: Find the directional derivative of the function f = In (x² + y2) at the point P(4,5) in the…

A: By Bartleby policy I have to solve only first one as Q)3)a) and Q)3)b) are unrelated  problems.These…

Q: The directional derivative of f(x, y) = xe + cosxy at P,(2,0) in the direction of the vector 3i - 4j…

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Q: Find the unit vector u along which the rate of change of the function f(x, y) = x 2 + xy3 at the…

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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 +…

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Q: (B) At point (1,5), Find the Vector that is tangent and Normal to the curve: X' = 2y + 10

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Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) 5x sin(xy) at…

A: The given function isfx, y=5x.sin(xy)to find the direction in which the maximum rate of change…

Q: Find the directional derivative Duf(1, 1), where f(x, y) = x2 + y2 and u is the unit vector at an…

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

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Q: Find the directional derivative of f(x,y,z) = x²z – xz³ + zy at the point (1, -2,0)in the direction…

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Q: Find the work done by the force F = 4xyỉ + (2x2 - 3xy)j by pushing a particle along the line segment…

A: Step:-1 Given Force is F→ =4xy i→ +2x2 -3xy j→ Here, given that particle moves along the line…

Q: What is the directional derivative of f(x, y) = 4xy+ y cos x at the point (0, 1) in the direction of…

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Q: Compute the directional derivative and gradient of at (2,-1,0) in the direction of the unit vector…

A: Dot product of A.B is ad+be+cf where A=<a,b,c> and B=<d,e,f>.