Kazakhstan Institute of Management, Economics and Strategic Research
Calcul
ECON 1021

Spring 2012
1. (max 10 pts) Find local extreme points for
f ( x, y ) x 3 y 3 3 xy 17
f ( x, y ) 2 x 3 2 y 3 6 xy 15
f ( x, y ) x 3 y 3 3xy 15
f ( x, y ) x 3 8 y 3 6 xy 1
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2. (max 10 pts) Find f x , f y , f xx , f yy and f xy for
f ( x, y ) x y
xy
f ( x, y )
Kazakhstan Institute of Management, Economics and Strategic Research
Calcul
ECON 1021

Spring 2012
Lecture#11
Infinite Sequences and Series of functions
Let u n (x) n 0,1,2,. be a sequence of functions
defined in a, b . The sequence is said to converge to
F (x) , or to have the limit F (x) in a, b , if for each
x in a, b the sequence of numbers u n (x)
Kazakhstan Institute of Management, Economics and Strategic Research
Calcul
ECON 1021

Spring 2012
I. Apply Cramers Rule to solve the following systems of linear equations
1.
3 x 8 y z 25
2 x 3 y 2 z 2
x 2 y 2 z 1
2.
y 5 x 3 z 1
z x 3 y 3
y 2 x 5 z 8
II. Apply Method of Inverse Matrix to solve the following systems of linear equations
3.
2 x z 1