Vector-valued function R(t) = <3cos2t, 9t, -3sin2t> 1. Reparametrize R using the directed arc length s from the reference point P (3, 0, 0) in the direction of increasing values of t.

Q: cost-sint) √2 r(t) = (3e' cost)i + (3e¹ sint)j + 2k For the space curve below, T= i+ sint+ cost s!).…

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Q: In words, describe the curve r(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to a -- give enough…

A: To Explain: The parametric curve is r(t)=(2sint,et,2cost) for 0≤t≤6π , so that its graph can be…

Q: time t = 0. Find two distances between the points r(1) and r(2): the Euclidean distance in space and…

A: Use the formula for the Euclidean distance and distance along the curve .

Q: Find the domain of r(t) and the interval(s) on which the vector- valued function is continuous. r…

A: We need to find the domain and the interval on which the vector-valued function is continuous.

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: 2. (a) Use Pythagoras' theorem to find the length of the line segment y = 2x from (1, 2) to (2, 4).…

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs for…

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Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: WHICH ANSWER IS CORRECT? Given the curve C parametrized by the vector equation r⃗…

A: Given :- The curve C parametrized by the vector equation r t = 3 sin t i^ +2 - sin t +cos t  j^…

Q: Consider a differentiable function p(x,y) with the properties below. Use these properties to answer…

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Q: The unit tangent I already found which was correct was (32 , 24t , 9t^2 )*1/41 I need the…

A: To find unit normal vector

Q: Describe the trajectory velocity and acceleration of the parametric curve r(t)= establish if  r(t)…

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Q: The position vector of a particle is (a) Find the length of the curve for 1≤t≤4 (b) Find parametric…

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Q: A particle travels along the curve r(t) = (cos t, sin t, In(cos t)). a) Find the distance the…

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Q: Given the vector-valued function r (t) = e-t i +t j +(tan t) k Find: a) r'(t) b) r"(t) c) r'(t) .…

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