2. Consider the plane curve r(t) = <2cos(t),3sin(t)>. Parameterize the osculating circle at t=0. Sketch both...

2. Consider the plane curve r(t) = <2cos(t),3sin(t)>. Parameterize the osculating circle at t=0. Sketch both the curve and the osculating circle

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Colby Messinger answered 2 years ago

r(t)=sinti+costj. - Sketch the plane curve represented by r and include arrows indicating its orientation. -...

r(t)=sinti+costj. - Sketch the plane curve represented by r and include arrows indicating its orientation. - Sketch the position vector r(t), the velocity vector r′(t), and the acceleration vector r′′(t) for the two times t = π/2, 5π/4 , putting the initial points of the velocity and acceleration vectors at the terminal points of the position vectors. - Prove that the vectors r(t) and r′(t) are orthogonal for every t.

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Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating...

Let ¯r(t) = < t, t^2 , t^3 >be a twisted cubic. a) Find the osculating circle for this twisted cubic at t = 0. b) Try to do the same for the ordinary cubic parabola ¯r(t) = <t, 0, t^3 >. Explain why did you fail to do that.

Given the curve −→r (t) = <sin3 (t), cos3 (t),sin2 (t)> for 0 ≤ t ≤...

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Given the curve C in parametric form : C : x = 2cos t , y...

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Q2a) Consider a transformation T : R 2×2 → R 2×2 such that T(M) = MT...

Q2a) Consider a transformation T : R 2×2 → R 2×2 such that T(M) = MT . This is infact a linear transformation. Based on this, justify if the following statements are true or not. (2) a) T ◦ T is the identity transformation. b) The kernel of T is the zero matrix. c) Range T = R 2×2 d) T(M) =-M is impossible. b) Assume that you are given a matrix A = [aij ] ∈ R n×n with...

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