s11wk06su - Math 23 B. Dodson Week 3a Homework: 13.3...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Math 23 B. Dodson Week 3a Homework: 13.3 curvature (using differentiation, formula(9)) 14.2 limits 14.3 partial derivatives, 2nd order deriv Week 3a Homework: (continued) 13.3 curvature Problem 13.3.16 Use formula (9) to find the curvature of vector r ( t ) = < t 2 , 2 t, ln t > . Solution: We start with part (a), find the unit tangent vector T and principal unit normal vector N. We compute vector r = < 2 t, 2 , 1 t > and | vector r | 2 = 4 t 2 + 4 + 1 t 2 = (2 t + 1 t ) 2 , so | vector r | = 2 t + 1 t (since t > , is used for ln t ). 2 . We also simplify 1 | vector r | = t 2 t 2 + 1 , then vector T = 1 | vector r | vector r = t 2 t 2 + 1 < 2 t, 2 , 1 t > . Using the product rule, vector T = parenleftbigg t 2 t 2 + 1 parenrightbigg < 2 t, 2 , 1 t > + t 2 t 2 + 1 ( < 2 t, 2 , 1 t > ) = parenleftbigg (2 t 2 + 1) t (4 t ) (2 t 2 + 1) 2 parenrightbigg < 2 t, 2 , 1 t > + t 2 t 2 + 1 parenleftbigg < 2 , , 1 t 2 > parenrightbigg = parenleftbigg 1 (2...
View Full Document

This note was uploaded on 11/24/2011 for the course MATH 23 taught by Professor Yukich during the Spring '06 term at Lehigh University .

Page1 / 5

s11wk06su - Math 23 B. Dodson Week 3a Homework: 13.3...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online