Consider the R − R 2 function r defined by r (t) = ￾ t, t2
; t ∈ [−3, 3] . (a) Determine the vector derivative r 0 (1) (b) Sketch the curve r together with the vector r 0 (1), in order to illustrate the geometric meaning of the vector derivative.

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Q: (a) Find the direction for which the directional derivative of the function f(x, y, z) = √√x² + y² +…

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A: Tangent vectors and vector perpendicular to them

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A: if r'(t) = 0 then we can say that r'(t) is perpendicular to the function r(t) for all times t.

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A: Here to find the directional derivative at (a, b) of fin(x, y) the direction of unit vector u, v and…

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,…

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A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

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: 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: 1. Let ř(t) = (In |t – 1|, e', vi ) (a) Express the vector valued function in parametric form. (b)…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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: - r(t) = (81²)i + (5t − 2) ƒ + (81³) k at - at t = 7.

A: Please see the below picture for detailed solution.

Q: ) Find the directional derivative of the function f(x, y) = sin²(xy) at the point P (2,7) -2i+j √5…

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