My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
September 19th, 2018, 08:08 PM   #1
Senior Member
 
Joined: Apr 2017
From: New York

Posts: 119
Thanks: 6

equation of a tangent line

Compute an equation of the tangent line to the curve q(s) = (s,sin(πs^2),cos(3πs^2))at the point (2,0,1) where s∈R

in this questions my steps will be these:
step1: match x,y,z components of the point and q(s) to find parameter s
step2: find q'(s)
step3: insert parameter s into q'(s) to find the point of tangency

step 4: equation of tangent line is what in 3D?
y-y1=m(x-x1) in 2D
Leonardox is offline  
 
September 19th, 2018, 10:17 PM   #2
Senior Member
 
Joined: Apr 2017
From: New York

Posts: 119
Thanks: 6

This is the work I have done.
Attached Images
File Type: jpg 85747C8B-181E-4A29-A969-8C0D4D50EDAE.jpg (20.6 KB, 3 views)
File Type: jpg D9CAFF95-10F3-4F07-A02B-D8847043948E.jpg (19.7 KB, 2 views)
Leonardox is offline  
September 20th, 2018, 09:33 PM   #3
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,200
Thanks: 1155

you seem to be misunderstanding this a bit

$q(s) = (s,~\sin(\pi s^2),~\cos(3 \pi s^2)$

$p=(2,~0,~1) \Rightarrow s=2$

We find the tangent vector at $p$ by differentiating $q(s)$ and letting $s=2$

$\dfrac{dq}{ds} = (1,~2 \pi s \cos \left(\pi s^2\right),~-6 \pi s \sin \left(3 \pi s^2\right))$

$\left . \dfrac{dq}{ds}\right|_{s=2} = (1,~4 \pi ,~0)$

and our unit tangent vector at $p$ is thus

$T = \dfrac{1}{\sqrt{16\pi^2 + 1}}(1,~4\pi,~0)$

and the equation for our line is simply

$\ell(u) =uT + p$

$\ell(u) =\left( \dfrac{u}{\sqrt{1+16 \pi ^2}}+2,~\dfrac{4 \pi u}{\sqrt{1+16 \pi ^2}},~1\right)$
romsek is online now  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
equation, line, tangent



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Equation of a tangent line frazza999 Pre-Calculus 6 June 25th, 2014 03:58 PM
equation of a tangent line unwisetome3 Calculus 2 October 28th, 2012 07:52 PM
Tangent line equation kevpb Calculus 3 May 25th, 2012 11:32 PM
Equation of the tangent line arron1990 Calculus 5 February 9th, 2012 02:29 AM
Tangent Line Equation RMG46 Calculus 28 September 28th, 2011 10:21 AM





Copyright © 2018 My Math Forum. All rights reserved.