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 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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