Notes for calc 3 class, Summaries of Calculus

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MIDTERMZ_ Domainsoffunctions Reef F needs 70 Luc needs^0

need o

of flour Fte

need

110

and

Ite either

or a (^) y O it I

LEVELCURVES.ee Sketch (^) the level (^) curves (^) of flu (^) y

y

fe It Try C O CH (^0 1) first CI (^) Yi Se^ is^ y k

I

7 the both (^) together Y re

form a^

y

I (^) 4th us^ y l f Ife 1 be

N (^) ENTLINESANDTANGENTPLAN.es TAEN LEcrvessorFacesi

D Tangent line to

flay α (^) at a b is x a^ y b If a^ b D IDI Tangent^ plane to^ flu^ y^ z^ α (^) at a (^) b c is x a^ y b z c^ Yf a (^) b c^0 of Tangent (^) plane to^22 4 42 at^ 0,1 1 flay z k (^) Y 2 then the (^) surface is

flu 4,27 0

Now If 0,1 1 2n

2y (^227) 40,2 2 eqn is^ k^01 y 77

214 1 2 (^2 1 )

22 0 E

IFFERENTIASApproximationslerrors.se betty dg 0.05 0. what is^ dz In

ten 1

dz 8 In de 2 dat T.de dz dy

It

ms dz

iEZEhEaEM

LimiTs

hi

O

t t.EE make 1 y ms helm (^) y y as (^) a (^) y (^) 0, chico Y E

lay sm (^) 141.141 m

Exel 141

h

ay lal.ly^ Ilxyl^8 as (^) x (^) y 10,

hero f r Cos^ r I r^ cos3o^ sm3o Ir corotsmsol^ r^ cosso^ senso r cossol (^) 15m 22 halnie 12Th of (^) play ath^

h aty

t nty (^0) as 4,47 0, E the 1, t