Re: Evaluating the limit
- From: quasi <quasi@xxxxxxxx>
- Date: Sun, 30 Mar 2008 18:22:22 -0500
On Sun, 30 Mar 2008 14:46:55 -0700 (PDT), conrad <conrad@xxxxxxxxxx>
wrote:
My book evaluates the limit:
lim_{x->0} (|2x - 1| - |2x + 1|)/x
It offers the following reasoning:
For -1/2 < x < 1/2, we have 2x-1 < 0
and 2x + 1 > 0, so |2x - 1| = -(2x - 1)
and |2x + 1| = 2x + 1
lim_{x -> 0} [-(2x - 1) - (2x + 1)]/x = lim_{x->0} -4 = -4
What I fail to understand in their reasoning is
why consider |2x - 1| for values less than
zero but |2x + 1| for values greater than zero?
I thought that both |2x - 1| and |2x + 1| should
have been considered for values less than 0
then |2x - 1| and |2x + 1| should have been
considered for values greater than zero.
On the interval -1/2 <= x <= 1/2, graph just the numerator,
g(x) = |2x - 1| - |2x + 1|
Use a table of values, if necessary.
Then read once again the author's reasoning (which is perfect) about
the values of g(x)/x on the interval (-1/2, 1/2)
quasi
.
- References:
- Evaluating the limit
- From: conrad
- Evaluating the limit
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