Docsity
Docsity

Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity


Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan


Guidelines and tips
Guidelines and tips

Tangent planes and normal lines (basics and problems), Lecture notes of Applied Mathematics

Description:Tangent planesand normal linesare fundamental concepts in calculus and differential geometry that help us understand the behavior of curves and surfaces.In the context of curves, a tangent line represents a line that touches the curve at a specific point, sharing the same slope as the curve at that point. It provides information about the instantaneous rate of change or the direction of motion at that point. Tangent lines play a crucial role in finding derivatives, determining critical points, and understanding the local behavior of curves.On the other hand, normal planes are relevant in the study of surfaces. A normal plane is a plane that is perpendicular to the tangent line at a given point on the surface. It serves as a reference plane, helping us understand the orientation and behavior of the surface at that point. Normal planes are important in various applications, such as determining surface normals.

Typology: Lecture notes

2022/2023

Available from 05/17/2023

mahesh-5
mahesh-5 🇮🇳

1 document

1 / 14

Toggle sidebar

Related documents


Partial preview of the text

Download Tangent planes and normal lines (basics and problems) and more Lecture notes Applied Mathematics in PDF only on Docsity! Targen planes and mor ma Mroeg trreormet SCAR Wwrke greta Cc ComckBh om al Liao SOAR Supeses]S Rex, Sy = c °° Yn & Yene\ CANN GS ort whe concen -ecns SHAQ‘ FASS eg, Baxcugh a eats (xo, 2) te Stee s= & were « = FceX) and 3 gts) * Wren ALE Fev eri ads wae Ss ee Ve get =O ax “ae 24° Ake consaey enakevle ak FF 1e sw Cx) = oe ~ \ak and ass Vek 4 =e y) Va IY ane WO) = S254 aS3 Ate aT weve oth Ae AVE LA a an at Sy =" Trak Means Wie weckoay WE G.,y .) p3a Serco kaar ee ks aad met al Mr & Verner’. pSearscess 7 ~Y Qradtier, ie ome bk aice® eben Grek =~ = LEAS C Vomctiom GV Luo soniotles) _ | \ core Suppose Pex, Qyac LS Yn & Nene Carty © nce FASS a> ce &S Cre tue\= — OF We SKumctiom 4 = CxS Manag, Q Pant (xo, 92) Wene wc = Feary and y= 90k) _ Hen AV hevermtiating wane he LSS get SIF AKL AL AS = Sse GC Consider esravient ek F te we Cas) (af & \oee Ve anak O\es \ek N=) Vx oy qhen ng CED = a 7 & AY 5 vA tc 7 Ac WEN = DE. Se PE AQ EG “d= ae” Sy St Thakmeans The Vveckoayv WE Ges ,4e) eamad ec ~IE \ Rey Wy Woke o Say _ 2 ch ak © > ve e Css AD =) , : : MOA Pees, te) Oe sea =e" Sree eR pe a ( Agee Chane and 8 mf and “oe een 7 TW, . yecke™ em Bria Necker Garakien F x ant 7 Lee Kangen eXada TEL xese 25) w= oS EA ose of Lamoernic etane - Le¥ p2,5e,40) Soe a Pont am Sse oNaeh Pot roxy wy = o where TE ga. WHE cart SQ oarsamr ck Yas Lmarngen: gian= ax Pe ,S SC e ses) Cree eos, 29) Cy-se), ~ NS Cx. 72 G2.) = ot Ye EAAQerve ok SUA SEV | mrad AN SQeasor plane Eo the seh ak ov) > oa Oe A) wee f= Verh = \ ot kore oe 3 . > Wea Ee Then \eve Ogg Wesel Fs oa pe von = 2 Fy = - Sy y= AS Be Co.) = uw Fy = -—@ Tre. = 6 Pind an equabien ef bo Leaangecctk plane ta the Sra Se ELE FES =a jo ie ae Bux Rand AN eyes Co R vectay Rormrctian of Awso oF Ako eee Noon cob ee 3S AVGSG Kou aS Neko Yield Q axnbct ¥ = Vx e(io_ +3 2 te Se i Ay Mewes) x 5 * 2 2 @ Doe OWN Aw il eae A Necksv LielA Fis SAXA*ES oe WAGE GR) | aT cont - a of Whe veckeon Keka 3 LS — x = , Qs ax Y.s ve = Wey (B+ 3 Be 2s \ ae Ce +Qyx ~Re chivergence ~ TAP ,DBB®_ Be oN waa ee NR eee ree BEN Ye, Yer eles TEN ESOT BA oy an SMe\ie es Ee cava ComeOt@ Wig. R Cas” vers Qerrce. exer sh 4 ab TOUS SSeS ae Se © Ore ras ~AY or Y= \\ rm ) ul N | 3 4 es Ww { 8 ag " f u 3 Nv a= ‘ = ee a on] \ \ AYES ae CGyal- 2 ,—- 2 2. = ax-ya BE * DKK = -2+4+R- 2 - + => -s = dace : 7 me AON SS Q Trews Siete = . Awe v =3 camnck Cant = % A) Avev = Vex ee
Docsity logo



Copyright © 2024 Ladybird Srl - Via Leonardo da Vinci 16, 10126, Torino, Italy - VAT 10816460017 - All rights reserved