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Examination Notes: Multivariable Calculus - Mathematics 206a - Mr. Haines, Exams of Mathematics

Baddi University of Emerging Sciences and TechnologiesMathematics

The questions and solutions for examination #1 of the multivariable calculus course taught by mr. Haines in mathematics 206a during the academic year 2009. Questions on sketching the domain of a function, finding the equation of a line, partial derivatives, vector dot product, limit calculation, symmetric matrix, level curves, plane equation, and parallelogram properties.

Typology: Exams

2012/2013

Uploaded on 03/07/2013

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NAME_______________________________________
I____II____III____IV____V____VI____VII____VIII____IX____X____TOTAL ___________
(10) (10) (16) (16) (6) (10) (10) (8) (8) (6)
February 5 Mathematics 206a Mr. Haines
2009 Multivariable Calculus
Examination #1
(10) I. If f : R
2
→
R
3
with rule f (x, y) =
(
)
2
,4, xyye
xy
−−
,
sketch a graph of the domain of f .
(10) II. Give an equation of the straight line passing through the points (1, 2, 3) and (3, 6, 7).
pf3
pf4
pf5

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NAME_______________________________________

I____II____III____IV____V____VI____VII____VIII____IX____X____TOTAL ___________

February 5 Mathematics 206a Mr. Haines

2009 Multivariable Calculus Examination #

(10) I. If f : R 2 → R 3

with rule f ( x, y ) = ( )

2 e , 4 y , y x xy − − ,

sketch a graph of the domain of f.

(10) II. Give an equation of the straight line passing through the points (1, 2, 3) and (3, 6, 7).

(16) III. If ( , ) ln( )

2 2 f x y = x + y

A. =

( x , y ) x

f

B. =

( x , y ) y

f

C. =

2 x y y

f

D. =

2 x y x

f

(6) V. Explain why (^22) (,) ( 0 , 0 )

lim x y

xy x y → +

does not exist.

(10) VI. For the quadratic form p ( x , y , z ) x 5 y 10 z 6 xy 4 xz 2 yz 2 2 2 = + − + − + ,

A. give a symmetric matrix S that is the matrix of this quadratic form.

B. By taking determinants and using Sylvester’s Theorem, determine if p is positive definite, negative definite, indefinite, or none of these.

(10) VII. If f : R

2 → R with rule (^2)

2 ( , ) x

y f x y = , sketch the level curves of f for c = 0, 1, 4,

and 16.

(8) VIII. Give an equation of the plane through the point (1, 2, 3) with normal vector parallel to

the line with equation ( x , y , z )= ( 2 t + 1 , 5 t − 7 ,− t + 8 ).