differential geometry questions (2342)

I need to solve question 13 on page 19 from the attached book:

"Suppose ¤ 0 at P. Of all the planes containing the tangent line to ˛ at P, show that ˛ lies locally

on both sides only of the osculating plane."

p21 Shifrin: Question 20 ("Two distinct parametrized curves...")

p32 Shifrin: Question 8 ("Let C be a C2 closed space curve, say parametrized by arclength...")

p. 33: Question 12 ("Generalize Theorem 3.5 to prove that if C...")

Please give full solutions, typed in Word.

I need it within 2 days.

My budget is $20.

Habilidades: Engenharia, Matemática, Matlab and Mathematica, Engenharia Mecânica

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