Mimic the argument in the reading for this section to argue that a reasonable definition for the arc length of a parametric curve $\left(x\right(t),y(t\left)\right)$from $t=a$to $t=b$is

$\underset{n\to \mathrm{\infty }}{lim} \sum _{k=1}^n \sqrt{{\left(\mathrm{\Delta }{x}_k\right)}^2+{\left(\mathrm{\Delta }{y}_k\right)}^2},$

where $∆x_k$and $∆y_k$are defined as in the previous problem.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with Vaia!