hwsol_11

hwsol_11 - Homework Assignment 11 - (11.5) - Solutions Page...

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

View Full Document Right Arrow Icon
Homework Assignment 11 - (11.5) - Solutions Page 902: 6*, 10*, 14*, 16*, 18*, 20*, 22*, 26*, 29-32, 34*, 41(extra points), 42(extra points) *Let r(t) ! (t,sin(t),2t). Find the radius and center of the osculating circle at t ! pi/2. 6. r " ! t " !# t , t 3 $ , t ! 0, t ! 1 r " % ! t " !# 1,3 t 2 $ , r " % ! t " ! 1 & 9 t 4 , T " ! t " ! 1 1 & 9 t 4 # t 2 $ T " ! 0 " !# 1,0 $ , T " ! 1 " ! 1 10 # $ T " % ! t " ! ! 36 t 3 2 ! 1 & 9 t 4 " 3/2 # t 2 $& 1 1 & 9 t 4 # 0, 6 t $ ! 1 ! 1 & 9 t 4 " 3/2 # ! 18 t 3 , ! 54 t 5 & 6 t ! 1 & 9 t 4 " $! 1 ! 1 & 9 t 4 " 3/2 # ! 18 t 3 ,6 t $ T " % ! 0 " !# 0,0 $ , N " ! 0 " !# $ T " % ! 1 " ! 1 10 # ! 18, 6 $ , T " % ! 1 " ! 1 10 18 2 & 6 2 ! 6 N " ! 1 " ! 1 6 1 10 # ! 18, 6 $! 1 10 # ! 3, 1 $ 10. r " ! t " !# cos t , sin t , sin t $ , t ! 0, t ! ! 2 r " % ! t " !# ! sin t , cos t , cos t $ , r " % ! t " ! sin 2 t & cos 2 t & cos 2 ! 1 & cos 2 t T " ! t " ! 1 1 & cos 2 t # cos t , sin t , sin t $ T " ! 0 " ! 1 2 # 1,0,0 $ , T " ! 2 !# 0,1,1, $ T " % ! t " ! ! ! 2cos t sin t 2 ! 1 & cos 2 t " 3/2 # cos t , sin t , sin t 1 1 & cos 2 t # ! sin t , cos t , cos t $ ! 1 ! 1 & cos 2 t " 3/2 cos t sin t # cos t , sin t , sin t ! 1 & cos 2 " # ! sin t , cos t , cos t $ ! 1 ! 1 & cos 2 t " 3/2 # cos 2 t sin t ! sin t ! cos 2 t sin t , cos t sin 2 t & cos t & cos 3 t , cos t sin 2 t & cos t & cos 3 t $ ! 1 ! 1 & cos 2 t " 3/2 # ! sin t , 2cos t t $ T " % ! 0 " ! 1 22 # 0, 2,2 $! 1 2 # 0,1,1 $ , T " % ! 0 " ! 1 2 2 ! 1, N " ! 0 " ! 1 2 # $ T " % ! 2 !# ! $ , T " % ! 2 ! 1, N " ! 2 !# ! $ 14. r " ! t " !# t , t 3 $ , t ! 0 From Problem 6., we have the following r " % ! t " !# t 2 $ , r " % ! t " ! 1 & 9 t 4 , r " % ! 0 " ! 1 T " % ! 0 " !# $ , N " ! 0 " is not defined. 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Since T " % ! 0 " ! 0, " ! 0. So there is no osculating circle at t ! 0. 16. r " ! t " !# 2cos t , 3sin t $ , t ! ! 4 r " % ! t " !# ! 2sin t , 3cos t $ , r " %% ! t " !# ! t , ! 3sin t $ , r " % ! t " ! 4sin 2 t & 9cos 2 t r " % ! t " r " %% ! t " ! i " j " k " ! t 3cos t 0 ! t ! t 0 ! 6 k " , r " % ! t " r " %% !
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

hwsol_11 - Homework Assignment 11 - (11.5) - Solutions Page...

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