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by: Chandon Lim

25

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7

# Calculus III MATH- 2326-004

Chandon Lim
UTA
GPA 3.136

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these notes will be over Calculus III exam
COURSE
Calculus III
PROF.
Christopher Kribs
TYPE
Bundle
PAGES
7
WORDS
CONCEPTS
Math, Calculus III
KARMA
75 ?

## Popular in Applied Mathematics

This 7 page Bundle was uploaded by Chandon Lim on Tuesday April 5, 2016. The Bundle belongs to MATH- 2326-004 at University of Texas at Arlington taught by Christopher Kribs in Spring 2016. Since its upload, it has received 25 views. For similar materials see Calculus III in Applied Mathematics at University of Texas at Arlington.

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Date Created: 04/05/16
12.8 F(x,y)= 7sin(x)+2sin(y) 0=<x<2pi Fgrad=<7cosx,2cosy> Fgrad=0 cosx =o & cosy=0 X=pi/2,3pi/2 y=pi/2,3pi/2 (pi/2,pi/2) (pi/2,3pi/2) (3pi/2,pi/2) (3pi/2,3pi/2) 9 5 -5 -9 D=fxxfyy-(fxy)^2 =(-7sinx)(-2siny)-0^2 =-14 at (pi/2,3pi/2)& (3pi/2,pi/2) <0 therefore saddle points Arc Length, Curvature and Surfaces in 3-D Spaces Arc Length and Curvature ???? ???? ′ 2 ′ 2 ′ 2 Arc Length is a space curve described a ???? =∫????|⃗(????) ???????? = ∫???? √[???? ???? ] + [???? ???? ] + [ℎ ???? ] ( ) Where ????⃗ = f(t) ????̂ +g(t) ????̂ +h(t) ???? on a ≤ t ≤ b We can also write how far an object has traveled with respect to time t ???? s(t) ∫???? |⃗′(????) |???????? ex ⃗ ???? = 2????ȋ + ????ĵ + (1 + cos ???? ) ????̂ ′ ̂ ????⃗ ???? = 2ȋ + ĵ − sin(????) ???? 2???? 2???? ???? = ∫0 √ 2 + 1 + 1 ????????= ∫0 √ 5 + ???????????? (????)???????? ≈ 4.73 Ex Helix ̂ ⃗(t)=cos(t)ȋ + sin(t)ĵ + t ???? ̂ ⃗ ‘(t) = -sin(t)ȋ + cos(t)ĵ + ???? 13.2 This region is x simple and y simle V=integrandintegrand r dv =

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