Math 251, 2014, Summer 2 QUIZ 10 Grade_____/20 From 11.1 to 11.4 Name_______________________________________________ Work individually Show all work. No calculators. __________________________________________________________________________________________________ 1 1.        If , , , where , , , , , , , , u u x y z x x r s t y y r s t z z r s t    Follow the questions below to find an expression for . ) In the equation above, what is the dependent variable, what are the intermediate variables and what are the independent variables? ) There u s a b   are three intermediate variables and three independent variables. Each intermediate variable has a partial derivative with repect to each of the three independent variables. Give the three partial derivatives of each of the three intermediate variables (9 in total). Hint: one if them is . ) Each of these partial derivatives is a function of the three dependent variables. What are they y t c           ? Hint: , , so must also be a function of , , and . ) If was simply a function of its intermediate variables , and , the dependent variable would have three partial derivativ y y y r s t r s t t d u x y z        es. What are these 3 partial derivatives? Hint: one of them would be . ) Consider the partial derivatives in ( ). They are all functions of three variables. What are they? Hint: , u y e d u u x           , so must also be a function of , and . u y z x y z y       Math 261, 2014, Summer 2 QUIZ 10 2 of 3 ) There are three dependent variables and one independent variable. The dependent variable therefore has a partial derivative with respect to the each of the independent varibles. What are those par f tial derivatives? Hint: one of them is . ) We want to find where is the dependent variable we have selected. is constructed by applying the chain rule three times, once to each u t u g s s u s           derivative of with respect to each of the intermediate variables. What are the three chain rules that sum to make up ? Hint: for , the three chain rules are . . . u u s u u u x u y u t t x t y t z                    z t   ) Each partial derivative can be espressed as the dot product of two vectors. What is the dot product representation of ? Hint, . . . , , , , ) h u s u u x u y u z u u u x y z t x t y t z t x y z t t t i                                  Notice that , , is common to all the partial derivatives of the dependent variable with respect to the independent variable. What do we call , , ? u u u x y z u u u x y z             Math 261, 2014, Summer 2 QUIZ 10 3 of 3 2. 4 2 3 2 2 If , where , , sin , t t u x y y z x rse y rs e z r s t          ...

1. Math 251, 2014, Summer 2 QUIZ 10 Grade_____/20
From 11.1 to 11.4
Name_______________________________________________
Work individually
Show all work.
No calculators.
_____________________________________________________
_____________________________________________
1
Follow the questions below to find an expression for .
) In the equation above, what is the dependent variable, what
are the intermediate variables and
what are the independent variables?
) There
u

2. s
a
b
are three intermediate variables and three independent
variables. Each intermediate variable has a partial derivative
with repect to each of the three independent variables. Give the
three partial derivatives of each of the three
intermediate variables (9 in total). Hint: one if them is .
) Each of these partial derivatives is a function of the three
dependent variables. What are they
y
t
c
?

3. Hint: , , so must also be a function of , , and .
) If was simply a function of its intermediate variables , and ,
the dependent variable would
have three partial derivativ
y
y y r s t r s t
t
d u x y z
es. What are these 3 partial derivatives? Hint: one of them
would be .
) Consider the partial derivatives in ( ). They are all functions
of three variables.
What are they? Hint: ,
u
y
e d
u u x

4. u
y z x y z
y
Math 261, 2014, Summer 2 QUIZ 10
2 of 3
) There are three dependent variables and one independent
variable. The dependent variable therefore has a
partial derivative with respect to the each of the independent
varibles. What are those par
f
tial derivatives?
Hint: one of them is .
) We want to find where is the dependent variable we have
selected.

5. is constructed by applying the chain rule three times, once to
each
u
t
u
g s
s
u
s
derivative of with respect to
each of the intermediate variables. What are the three chain
rules that sum to make up ?
Hint: for , the three chain rules are . . .
u

6. u
s
u u u x u y u
t t x t y t z
z
t
) Each partial derivative can be espressed as the dot product of
two vectors.
What is the dot product representation of ?
Hint, . . . , , , ,
)
h

7. u
s
u u x u y u z u u u x y z
t x t y t z t x y z t t t
i
Notice that , , is common to all the partial derivatives of the
dependent variable
with respect to the independent variable. What do we call , , ?
u u u
x y z
u u u
x y z

8. Math 261, 2014, Summer 2 QUIZ 10
3 of 3
2.
4 2 3 2
2
If , where , , sin ,
t t
u x y y z x rse y rs e z r s t
2 22
2 22
0 00

9. find the value of when 2, 1, 0. 2, 2, 0
Hint: What are , , , , , , , , and what are the values of , , ?
What are , , ,
x xx
y yy
z zz
u
r s t x y z
s
u u u u u u
x y z x y z x y z
x y z x y z
x y
r s t
s

10. 2 2 2
1 1 1
0 0 0
, , , , , and what are the values of , , ?
What is in terms of , , , , , , , , , , , , , , , and , , ?
What is
r r r
s s s
t t t
z x y z
r s t r s t
s s s s s
u u u u x y z
x y z x y z x y z r s t r s t r s t
s x y z s s s

11. 2
2
2 2 2 2 220
2 2 1 1 122
0 0 0 0 001
0
2
2
0
2
1
0
in terms of , , , , , and ?
Evaluate .
x
y
x x r r rxz
y y s s syr
z z t t tzs

12. t
x
y
z
r
s
t
u u u u x y z
x x y z s s s
u
x

13. Research Overview
An important aspect of technology management is researching a
technology and identifying the implications of its adoption and
use with the company. This research paper will allow learners
evaluate a selected technology based on the identified
implications.
Research Components
Students will pick an emerging, innovative technology and
discuss the impact of the technology on business. The emerging
technology will be chosen early in the course and students will
spend the rest of the term researching the technology and
thinking about its application to the business processes.
Project requirements are:
· A project proposal, due in Module Two (6/29/2014), will be
submitted for feedback consistent with the Research Paper
Rubric, but not graded separately
· A brief midterm progress report, due in Module Five
(7/20/2014), will be submitted for feedback consistent with the
Research Paper Rubric, but not graded separately
· A final report, due in Module Nine (8/10/2014), will be graded
using Research Paper Rubric
Students can work in teams on the research project subject to
the instructor’s approval.

14. Research Paper Format
The final research proposal should be 10 pages in length, not
including cover page or reference list. This project must follow
APA formatting.
Research Objectives
To successfully complete this research project, you will be
expected to apply what you have learned in this course and
should include several of the following objectives:
1. Understand the impact of emerging IT trends on business
2. Understand the effect of IT on business models