Re: Evaluating the limit
- From: Raymond Manzoni <raymman@xxxxxxx>
- Date: Mon, 31 Mar 2008 00:27:30 +0200
conrad a écrit :
My book evaluates the limit:Ok
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.
--
conrad
We want a limit for x -> 0 so that
2x-1 -> -1 and 2x+1 -> 1
In the first case we need to evaluate the absolute value of negative values while in the second case we want the absolute value of positive values. The author choose to restrain x to the interval (-1/2, 1/2) so that he could conveniently remove the absolute values (fine idea!).
Hoping it helped,
Raymond
.
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- Evaluating the limit
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