[CHM 112] Quiz 7 question

[Andrew J. Pounds]

On 7/10/20 1:57 PM, wrote:
> Hi dr pounds. I’m still confused on what to put for the bound, and the
> x. Currently it’s 50/50 for me to get the right x. On quiz 7 when I
> type 1.11-((2x)^2)/((.5-2x)^2)(.5-x) 
>
> The bound should be {0,.5} right? Because .5 minus .5 is 0. But I end
> up getting .375 instead of the correct x value.
>
>

In your example the bound would be {0,0.25} because (0.5-2(0.25))=0.

Let me set up your example and provide my three rules for setting the
bounds and how to set the initial value of $x$.

Here is what you are trying to solve...

$1.11=\frac{(2x)^2}{(0.5-2x)^2(0.5-x)}$


To look for the bounds:

1. Isolate your search ONLY to the terms with negative signs in them. 
In this case that is $(0.5-2x)$ and $(0.5-x)$.

2. For both terms find the value of $x$ that makes the entire expression
in parenthesis equal to zero.  In this case it would be $x=0.25$ and $x=0.5$

3. Whichever one of these is SMALLER is your upper bound.   In this case
that is $x=0.25}.


Once you set the initial bounds you then have to set an initial value
for x.  ANY NUMBER between 0 and the upper bound should work there.  In
this particular example you could probably leave it at zero - or you
could set it to 0.1 which is what I would do.


> I don’t get the the thought process behind determining what the bound
> is.  Especially when a number can’t cleanly multiply to equal zero.
> For example the latest quiz had in the law of mass action, for the
> reactants, it’s ((2-3x)^2). I couldn’t find a clear number that would
> result in 2-2=0, so I did trial and error and I got lucky.  Can you
> think out loud for me? Surely there’s more to it than that. 

Hopefully my comments above helped with this.  In the case of an
expression like:

$(2-3x)$

think about doing the following...

$2-3x=0$

$2=3x$

$x=\frac{2}{3}$

That should work every time if the rest of your expression is set up
correctly in solver.

As always - keep asking if you are confused.


-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Director of the Computational Science Program
Mercer University,  Macon, GA 31207   (478) 301-5627

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