- #1
driscol
- 13
- 0
Homework Statement
Spivak's "Calculus" Chapter 1, Problem 4v
Find all numbers x for which
[tex]x^2-2x+2>0[/tex]
Homework Equations
The Attempt at a Solution
[tex]
x^2-2x+2>0
[/tex]
[tex]
x^2-2x>-2
[/tex]
[tex]
x^2-2x+1>-2+1
[/tex]
[tex]
(x-1)^2>-1
[/tex]
[tex]
x\in R
[/tex]
Would that be an adequate proof? Anything squared is always going to be positive...
Also, for these Spivak proofs, do I have to keep showing every single simple step?
[tex]
\frac{a}{b}=\frac{ac}{bc}\ \ \ \ \ \mbox{b,c\neq0}
[/tex]
[tex]
\frac{a}{b}=(\frac{a}{b})(\frac{c}{c})
[/tex]
[tex]
\frac{a}{b}=(\frac{a}{b})(1)
[/tex]
[tex]
\frac{a}{b}=\frac{a}{b}
[/tex]
I understand that doing this in the beginning will help me develop good habits/skills, but is it really necessary for every single problem? Could I just have canceled the c's in that equation without doing all the extra work?
Thanks.