MATH 182A Lecture 12: 10.2_calculus-with-parametric-curves

• School: RIT
• Department: Mathematics
• Course: MATH 182A
• Professor: Khan Akhtar

Document Summary

Calculus with parametric curves dy dx dy/dt dx/dt d2y dx2 = d dx(cid:19) dx(cid:18) dy dt(cid:18) dy dx(cid:19) dt d dx d dt ( dy dx ) dx dt. Using this, we can write the arc length function as: )2dx dy dx dy/dt dx/dt a r1 + ( =z b a p(dx/dt)2 + (dy/dt)2 a r( =z b dx dt dx/dt dy dt dx. Find dy x = t3 12t y = t2 1. = 3t2 12 = 3(t2 4) dy dt dx dt dy dt. 2 (3t2 12)(2) 2t(6t) (3t2 12)2. 6t2 24 12t2 (3t2 12)2 d dt dy dx d2y dx2 = d. 9(t2 4)2 dt ( dy dx) dx dt. Find dy dx: x = 2t3 + 3t2 12t y = 2t3 + 3t2 + 1. = 6t(t + 1) dy dt dx dt. 6t(t + 1) t(t2 + t 2) t(t + 1) (t + 2)(t 2)