Tagged Questions
0
votes
2answers
50 views
Prove That $|a +b| = |a| +|b|$ if $a$ and $b$ Have Same Signs, And $|a +b| < |a| + |b|$ if $a$ and $b$ Have Opposite Signs (Proved Differently) [duplicate]
My Proof:
This problem has mainly four cases, they are as follows:
1) $a, b > 0$
2) $a, b < 0$
3) $a > 0 > b$
4) $a < 0 < b $
Let suppose that the sum of the real numbers $a ...
0
votes
5answers
76 views
Prove That $|a +b| = |a| +|b|$ if $a$ and $b$ Have Same Signs, And $|a +b| < |a| + |b|$ if $a$ and $b$ Have Opposite Signs
My Proof:
$|a +b| = |a| +|b|$ ..... $(i)$
$|a +b| < |a| + |b|$ ..... $(i)$
If $'a'$ and $'b'$ have same signs:
Let $a$ and $b$ be equal to $-x$. Replacing $a$ and $b$ with $-x$ in the equation ...
2
votes
2answers
191 views
How to find critical points of an absolute values function
I am asked to find How many critical points does the function $g(x) = |x^2 − 4|$ have?
I know that the result is $3$ but I can only find $2$. What I do, is to equal the equation to $0$, so $x^2-4=0$ ...
0
votes
2answers
120 views
I can't find a absolute value function that have [-1,1] range
I want a function $f:\mathbb{R}\to[-1,1]$ with absolute value like $f(x)=|a-x|\ldots$ that have $[-1,1]$ range. Can anybody help me?
0
votes
0answers
51 views
Name for $\max(x, \frac 1x)$, $x > 0$? [duplicate]
Possible Duplicate:
Multiplicative Identity analog for absolute value
In looking for the most extreme scaling, I'm comparing $f(a)$ and $f(b)$ where $f(x) = \max(x, \frac 1x)$, $x > 0$? ...
1
vote
1answer
2k views
Limit with absolute value
I found this limit within the Calculus Single Variable book from Thomas.
$$ \lim _{x \to -2^-} (x+3) \frac{|x+2|}{(x+2)}$$
This is how I'm trying:
First of all, we need to found where the absolute ...
1
vote
4answers
205 views
Understanding $y=|mx+n|$
The diagram shows the graph of $y=|mx+n|$
(i tried my best to do the same thing as my exercise book, actually 1 is propotional to 1 and 3 is propotional to 3, but 2 is not propotional to 2)
Find ...
