[Date Index]
[Thread Index]
[Author Index]
Re: New user: Abs[] problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg50107] Re: [mg50079] New user: Abs[] problem
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Sun, 15 Aug 2004 03:14:38 -0400 (EDT)
*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst
*References*: <200408140550.BAA15327@smc.vnet.net>
*Reply-to*: murray at math.umass.edu
*Sender*: owner-wri-mathgroup at wolfram.com
Yes, sometimes Mathematica cannot find (all) solutions. But in this
case, BELIEVE! Mathematica DID solve it: there are no solutions!
You can see this, e.g., by graphing your piecewise-linear function:
Plot[x + 1 + Abs[2x - 4] + Abs[5 - x], {x, -10, 10}];
Plot[x + 1 + Abs[2x - 4] + Abs[5 - x], {x, 0, 5}];
(The second Plot is just to convince you that the minimum really is
strictly positive.)
Or, you can consider the 4 cases:
case1 = x >= 2 && 5 >= x;
case2 = x >= 2 && 5 < x;
case3 = x < 2 && 5 >= x;
case4 = x < 2 && 5 < x;
The first case gives the closed interval from 2 to 5; the second and
third simplify...
Reduce[case2, x]
x>5
Reduce[case3, x]
x<2
... and the fourth case gives the empty set:
Reduce[case4, x]
False
(You could have done that much without Mahematica, of course.)
Now look at your function of x on each of these intervals:
expr = x + 1 + Abs[2x - 4] + Abs[5 - x];
lin1 = Simplify[expr, case1]
2(1+x)
lin2 = Simplify[expr, case2]
4 (-2 + x)
lin3 = Simplify[expr, case3]
-2 (-5 + x)
Now try to solve the resulting linear equation in each case:
Solve[lin1 == 0, x]
{{x->-1}}
Solve[lin2 == 0, x]
{{x->2}}
Solve[lin3 == 0, x]
{{x->5}}
In each case, the line meets the x-axis at a point outside the interval
on which the corresponding line segment over the interval in question is
the domain of the piece. QED
Edson.Brusque at smc.vnet.net wrote:
> Hello,
>
> I'm starting Electrical Engineering and using Mathematica for
> helping me in Calculus e Algebra studies.
>
> I'm trying to solve this equation on Mathematica:
> x + 1 - |2x - 4| + |5 - x| = 0
>
> on the Math* notebook I'm typing:
> Solve[x + 1 - Abs[2x - 4] + Abs[5 - x] == 0,x]
>
> but only got an empty output: {{}}
>
> Someone please can help me get Math* to solve this?
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
Prev by Date:
**Re: Re: Smalest enclosing circle**
Next by Date:
**Re: Re: Smalest enclosing circle**
Previous by thread:
**Re: New user: Abs[] problem**
Next by thread:
**Re: Re: New user: Abs[] problem**
| |