2y Suppose f(x, y) = sin X in the direction of (1, 2). Then, 2y 2y i (a) ▼ f(x, y) = cos(2)21 +21) X (b) ▼ ƒ(6, π) = COS and u is the unit vector 1/2 ( - 1 3 ² + 1) i 18 3 (c) fu (6, π) = Du ƒ(6, π) = in 36 + 6

Q: Define two vector functions F(t) = 8 sin(t)i + 6 cos(t)j + (t – 2)k ü(t) = 6 sin(t)i + 8cos(t)j + (t…

A: We have to find the dot product of r(t) and u(t)

Q: 2. The position vector of a particle is given by r(t)= (2 cos t sin t)i +(cos^2 t - sin^2 t)j +…

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Q: Suppose f(x, y) = sin( (a) Vf(x, y) = = (b) Vƒ(3, π) = 2y x T 2y 2y 2y cos cos 2) Con (2) 200m (20 -…

A: Given that , fx,y=sin2yx and u is the unit vector in the direction of 1,1.

Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

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Q: If a particle's position vector is given by r(t) :: = (Use syntax like [2,3] for a vector.) 4 cos…

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Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

A:

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = 3 cos(t)i + 3 sin(t)j, to r'(t) =…

A: The given vector valued function

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

A:

Q: For the vector-valued function r(t) = (cos 2t, sin -(cos 2t, sin-4) 3 (4) what is the magnitude of…

A:

Q: 2 xy". - I + 3x'y". 2 →(2(3-t)(45+24)' ((33-t)"( 43+2€)² 6. Find the unit vector for which the…

A:

Q: #3. Consider the function xy2 if (x, y)# (0,0), f (x, y) = {x2+y2 if (x, y) = (0,0). Calculate the…

A: Given function is fx,y=xy2x2+y2if x,y≠0,00          if x,y=0,0 We have to calculate the directional…

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

A: Directional derivative of f(x,y) at any point P in the direction of vector v is, =(∇f)P.(unit vector…

Q: Suppose that the vector-valued function F(t) = < 3t, cos(5t), sin(5t) represents the position of an…

A:

Q: Show that (∂z/∂x)2 + (∂z/∂y)2 = (∂z/∂r)2 + (1/r2) (∂z/∂θ)2

A: The equation to be proved is,