Reparametrization to find arc length

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Homework Help Overview

The discussion revolves around reparametrizing a curve with respect to arc length, specifically for the curve defined by the vector function r(t) = [e^(2t)cos(2t)]i + 2j + [e^(2t)sin(2t)]k. Participants are exploring the process of finding the arc length from a given point.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss finding the arc length as a function of t and mention the importance of the derivative of the arc length concerning t. There is an indication that some are unsure about the next steps after calculating the derivative and its magnitude.

Discussion Status

Some participants have offered guidance on starting points, such as finding the arc length function and referencing calculus textbooks for formulas. Multiple interpretations of the problem are being explored, particularly regarding deriving the arc length formula.

Contextual Notes

There is a mention of using the Pythagorean theorem and Riemann sums to derive the arc length formula, suggesting that foundational concepts are being revisited. The original poster expresses uncertainty about the process after initial calculations.

llooppii
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Homework Statement



Reparametrize the curve with respect to arc length measured from the point where t=0 in the direction of increasing t.

r(t) = [e^(2t)cos(2t)]i+2j+[e^(2t)sin(2t)]k


Homework Equations



i know that the derivative of the arc length with respect to t = magnitude of the derivative of r(t).

The Attempt at a Solution



I found the derivative and found the magnitude, but am basically lost as of there.
 
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start by finding the arc length as function of t
 
Let s(t) be the arc length, and I'm sure Ur calculus textbook will have the formula of arc length..
 
In fact you can easily "derive" the formula with pythagorus theorem and riemman sum in mind.
 

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