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 November 13th, 2018, 05:05 AM #1 Senior Member   Joined: Dec 2015 From: Earth Posts: 817 Thanks: 113 Math Focus: Elementary Math Maximum value x and y integers $\displaystyle -2\leq x \leq 3$ $\displaystyle -3\leq y \leq 6$ Find maximum value of $\displaystyle \frac{x}{y}$ or max$\displaystyle [\frac{x}{y}]=$? November 13th, 2018, 06:23 AM #2 Senior Member   Joined: Sep 2015 From: USA Posts: 2,628 Thanks: 1469 there is no maximum value with $x \neq 0$, as y approaches zero $\dfrac x y$ becomes arbitrarily large. November 13th, 2018, 06:36 AM   #3
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Quote:
 Originally Posted by romsek there is no maximum value with $x \neq 0$, as y approaches zero $\dfrac x y$ becomes arbitrarily large.
$x,y$ seem to be integers so it should have a max.

@OP: Where are you stuck? This problem is pretty simple to just check every possible value of $x,y$. If you give it a moments thought you can also see that you can maximize the value of $x/y$ by maximizing the value of $x$ and minimizing the value of $y$. Do this also for $-x/y$ and take the larger of the two. November 13th, 2018, 02:06 PM #4 Global Moderator   Joined: May 2007 Posts: 6,850 Thanks: 742 Since $y=0$ is allowed, there is no max, since dividing by $0$ will lead to trouble. November 13th, 2018, 05:20 PM   #5
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 Originally Posted by mathman Since $y=0$ is allowed, there is no max, since dividing by $0$ will lead to trouble.
Are you implying that $\frac{x}{0} = \infty$? I assume this is undefined and thus there is no trouble. November 14th, 2018, 02:31 PM #6 Global Moderator   Joined: May 2007 Posts: 6,850 Thanks: 742 For this question $\infty =$ trouble. November 14th, 2018, 06:22 PM #7 Senior Member   Joined: May 2016 From: USA Posts: 1,310 Thanks: 552 I think the problem is underspecified. It is unclear whether zero as a denominator is excluded or included from consideration. If it is included, a rational maximum does not exist. If it is excluded, a rational maximum does exist. What is the question? November 15th, 2018, 11:05 AM #8 Senior Member   Joined: Dec 2015 From: Earth Posts: 817 Thanks: 113 Math Focus: Elementary Math Let $\displaystyle y\neq 0$ $\displaystyle z=\frac{x}{y}$ , symmetry $\displaystyle z(-x,-y)=z(x,y)$ defines the nature of $\displaystyle x,y$ , so x and y must be both negative or positive So max$\displaystyle [\frac{x}{y}]=max[\frac{|x|}{|y|}]$ or we can work with the new function $\displaystyle z_1=\frac{|x|}{|y|}$ max$\displaystyle [\frac{x}{y}]=\frac{max[|x|]}{min[|y|]}=3$ November 15th, 2018, 11:10 AM   #9
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Quote:
 Originally Posted by mathman For this question $\infty =$ trouble.
Yes, infinity is trouble. But division by zero doesn't equal infinity. Tags maximum Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Mcfok Trigonometry 2 July 15th, 2015 01:46 PM Monox D. I-Fly Pre-Calculus 4 October 13th, 2014 06:58 AM rakmo Algebra 2 November 8th, 2013 03:29 AM servant119b Algebra 2 June 7th, 2012 03:27 PM Roberth_19 Calculus 4 April 3rd, 2010 03:47 PM

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