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February 20th, 2017, 04:03 AM   #1
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Curve

Hi!

I got some problems understanding this math task, so would appreciate all help I could get!:

Task: Let σ(t) be the curve σ(t) = cos(t)i + sin(t)j, and put r(t) = e^(-t)
*σ(t).

a) Sketch the curve r(t) for t ∈ [0, 4π]
b) Find the lenght of the segment r(t) for t ∈ [0, ∞)
c) Show that r(t) satisfies this differential equation:
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February 21st, 2017, 04:46 AM   #2
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Have you not even attempted this? You are given that and . Calculate a number of (x, y) values and plot them. If you are really lazy, you can use the graphing program at https://www.desmos.com/calculator. Enter (e^(-t)cos(t), e^(-t)sin(t)) as the function to be graphed.

If a curve is given as parametric functions, x= f(t), y= g(t), then the arc length, from to is given by . What do you get for that integral?

I cannot see the differential equation it is supposed to satisfy. Did you try just finding the derivatives and putting them into the equation?

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