Find r'(t), r(t), and r'(to) for the given value of to- r(t) = (e², e²t), to = 0 r'(t) = r(to) = r'(to) = Sketch the curve represented by the vector-valued function, and sketch the vectors r(t) and r'(to). y 2 X X x Z (1, 1) 1 1 (1, 1) (0, 1) r (1,0) 1 1 -1

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = (et, e24), to = 0 r'(t) = r(t) =…

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Q: (a) Find the directional derivative of z = x²y at (5,5) in the direction of π/2 with the positive…

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

A: Here, f(x, y, z) is given we have to find directional derivative of f(x, y, z) at point (2, 1,2) in…

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

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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: #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…