Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(t) , sin(3t) , sin( when t Velocity: Acceleration: Speed: Usage: To enter a vector, for example (x, y, z), type "< x, y, z >"

Q: Find the maximum rate of change of f(x, y) = ln(x² + y2) at the point (-3, -5) and the direction in…

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Q: Find the directional derivative of f (x, y, z) = 2z²x + y³ at the point (2, 2, 1) in the direction…

A: Here we have to find the directional derivative for given f(x, y, z).

Q: Determine the domain of the vector function r() = cos(4t) i + 7in(t - 5) J - 10 Evaluate if the…

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Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: As per given by the question, there are given: a→t=6t, 5sint, cos6tv→0=4, 3, 5r→0=3, -4, -4 Now, For…

Q: Find the directional derivative of the function f(, y) = In(x + y°) at the point (- 1,3) in th…

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Q: (플몰) V2 v2 2' 2 f(x, y) = x² – 3y², u и —

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Q: (a) F(t)=(2 sint)i + (2 cost)j from the point A(2, 0) to the point B(-2, 0)

A: To find the arc length of given function

Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: The vector describing a particular particle is given by F (t) = Rcos (wt) î + R sin (wt) ĵ, where R…

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Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: Find the Directional derivative of the function f(x,y,z) = /x² + y² + z² from point (1,2, –2) in the…

A: The objective is to compute the directional derivative of the function fx,y,z=x2+y2+z2 from point…

Q: (b) Find the directional derivative, Daf(2, 9) where u is a unit vector in the direction of i = 31-…

A: (a) Consider the function fx, y=xy. This gives ∇fx,y=i∂∂x+j∂∂y fx,y=i∂f∂x+j∂f∂y=yi+x2yj   At 2, 9,…

Q: ū = (-/3, –1) and w = (1, /3) E. |

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

A: Here we use the formula, Dvf(x,y)=∇f(x,y).v

Q: The motion of a point on the circumference of a rolling wheel of radius 5 feet is described by the…

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Q: Find Components of the Acceleration For the curve defined by T(t) = (e-t cos(t), e' sin(t)) |3D find…

A: To find- For the curve defined by r→t = e-tcost, et sint, find the unit tangent vector, unit normal…

Q: Find the vector equation of the tangent line to F(t) = 2 (el-t) In t i+ tan-tj+ k at cos(t m) the…

A: Answer is mentioned below

Q: Given u(t) = (e',e-t). a) Find: (i) u'(t) (ii) u"(t) b) Find the unit tangent

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