Math 127(3) - Warren D. Smith - Homework #1 - due Tues 28 Jan 2003
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Read ch 12. 
Check out the math127 web page attached to my home page
    http:/math.temple.edu/~wds.
This and future homeworks are available on that page!!
Important! Remember this web page!

Problems 1-4 review your (hopefully background) knowledge
for this course. Prob 5 covers stuff in the book.

1. For the real-valued function F(x)=sqrt(sin(x)) on the real 
numbers:
a. What is the range of F?
b. What is the domain of F?
c. Find a maximum of F?


2. Find the derivatives (d/du) and integrals (du from 0 to x) of 
these functions:
                    2
a.    F(u) = u sin(u )

              2
b.    F(u) = u  sin(u).


3. (Complex numbers.) Let i be the square root of -1.
What is   (1+7i) / (3+4I)  ?
         

4. Solve the following system of 3 equations for the 3 unknowns
x,y, & z  (get exact rationals as answers):
            3x-7y+z = 8
             x+y    = 9
            5x+2y-z = 1

5. Do exercises 2,8 and 30 page 803 (exercises for sec 12.3) in the 
book.

FOR THOSE WITHOUT THE BOOK, THIS SECTION WAS TITLED "DOT PRODUCTS" AND

2:    compute (4,2,-1) . (-2,2,1)

8:   a . (a-b) - b . (b+a)    where a,b vectors

30:   what can you conclude about vectors a and b if
     2      2        2
  |a|  + |b|  = |a+b|

and what if instead
     2      2        2
  |a|  + |b|  = |a-b|  ?