# justifying

1. ### Justifying an extreme value theorem?

I was looking through the coursework document on college board and one sentence says there are three ways to justify an extreme value. What are these three ways?
2. ### Help in justifying complex number question

Given Z1 and Z2 are two distinct complex numbers. If |Z1| = |Z2|, then Re \frac{z1+ z2}{z1 - z2} = 0 Is the above statement true or false? Show working to justify your answer. i managed to worked it out by letting z1= a+jb and z2= x+jy and then sub it in to work out and got true, not sure if...
3. ### justifying solutions of an equation

If I wrote ax^2+bx+c=0 --> x= d,e for example, then am I right in thinking that all this says is that d and e are the only possible solutions and that I would need 'iff' to justify that these are the solutions?
4. ### Justifying the integration of both sides

How can you prove using the definition of anti-differentiation, that if two functions are equal, then their anti-derivatives must differ by a constant? Also can this be used to prove the constant rule for integration??
5. ### Justifying the closure of a set

My problem is the following: Find \overline{A} \textrm{ for } A=\{(x,\sin(1/x))|x>0.\} I know that \overline{A}=A\cup\{(0,y)|-1\leq y \leq 1,\} but I need to figure out & understand the how'' behind that answer, in other words, give a proof that A-closure is that set above. Thanks.
6. ### justifying that a definition is "well-defined"

part a of this question was to show that similar matrices have the same trace, which i was able to prove without much difficulty. part b says, how would one define the trace of a linear operator T on a finite dimensional vector space? and how would one show that this definition is well-defined...
7. ### Justifying the Method of Undetermined Coefficients

I'm trying to "Justify the Method of Undetermined Coefficients" by using the "Annihilator Method." To start, I am given a linear, constant coefficient, nonhomogeneous differential equation: L[y] = g(x) Where L[y] = s_{k}*y^{k} + s_{k-1}*y^{k-1} + ... + s_{0}y [Note: y^{k} means the k'th...