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 February 20th, 2017, 04:03 AM #1 Newbie   Joined: Feb 2017 From: Norway Posts: 3 Thanks: 0 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:
 February 21st, 2017, 04:46 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Have you not even attempted this? You are given that $x= e^{-t}cos(t)$ and $y= e^{-t}sin(t)$. 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 $t_0$ to $t_1$ is given by $\int_{t_0}^{t_1} \sqrt{\left(\frac{df}{dt}\right)^2+ \left(\frac{dg}{dt}\right)^2}dt$. 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? $\frac{dy}{dx}= \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$

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