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## Calculus III

by: John MacGyver

8

0

1

# Calculus III MATH 241

John MacGyver
UT
GPA 3.52

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
1
WORDS
KARMA
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## Popular in Mathematics (M)

This 1 page Class Notes was uploaded by John MacGyver on Monday October 26, 2015. The Class Notes belongs to MATH 241 at University of Tennessee - Knoxville taught by Staff in Fall. Since its upload, it has received 8 views. For similar materials see /class/229828/math-241-university-of-tennessee-knoxville in Mathematics (M) at University of Tennessee - Knoxville.

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Date Created: 10/26/15
Math 241 Spring 2006 Alex Freire LIST 3 Tangent planes Taylor approximations classi cation of critical points maxmin 1 The temperature at the point z y is Tmy cos3 z 5 If you are at the point A 14 and you can go only with speed 4 in the direction of either P6 5 or Q5 7 in which direction is the increase of the temperature the highest 7 Answer toward Q 2 For the given function of two variables 1 and point P nd the rst order Taylor approximation at P ii an equation for the tangent plane to the graph of f at P 1 y 3144 PL 1 3 Find the linearization rst order Taylor approximation of the func tion of 3 variables 1 at the given point P 1 242 90y 2962 3242 P111 4Find the equation y m z b of the tangent line to the ellipse 2z2y2 9 at 21 Answer y 74m9 5 Find a unit normal 7 to the surface 3 2 7 4 y2 5 22 792 at the point P15 1 Answer 014 796024 6 Find the maximum of the function fzy 2 y 1712 3 my 7 1y2 716 on the segment joining P4 2 and Q1 5 Answer 12 7 Find a a quadratic approximation for the given function of two vari ables near the origin second order Taylor formula aw my 8 44 is acritical point offmy 2m23my1y2728z720y ls t 0 a local minimum or a local maximum of f43t 474t Answer local maximum 9 Let fzy 4z26my2y2728m720y Classify all critical points of 1 Answer saddle point at zy 2 2 10 Let 37x41y73m277my73y2 Classify all critical points of 1 Answer saddle point at zy 5 1

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