Help with problem

08102019, 10:01 PM
Post: #11




RE: Help with problem
(08042019 06:50 PM)levi98 Wrote: I took one look at this and realized the answer is A, and I'm with the several others who stated that X cannot be +5 or 5. Either value makes the denominator zero. When graphed by hand, it's clear that y becomes great without bound when: x > 5 y is therefore undefined if x = 5, as it's a real number (10) divided by zero. The graph shows y becomes great in the negative direction as x > 5 from less than 5 (e.g. 5.11), and it gets great in the positive direction as x > 5 from larger than 5 (e.g. 4.99). The principle being demonstrated here is why, by definition, any number (including 0) that's divided by 0 is undefined. The direction in which it's great without bound, + or , is indeterminate. It cannot be both simultaneously. There must also be a hole shown where x = 5, as it creates a denominator with the original quadratic that goes to zero. By definition, 0 divided by any number other than 0 is zero. Zero divided by zero, just like any other real number divided by zero, is also undefined. In other words, 0/0 is not equal to one. I believe that's the underlying principle here. At the limit where x > 5, y > 0.1, but that's not the same as x = 5. Plug in x = 5.1 and 5.01, and then x = 4.9 and 4.99 to see what you get. It converges on each side of 0.1 and there's an infinitesimally tiny hole for exactly x = 5. Zero is a special case that is neither a positive nor a negative real number. It has no "sign" like all other real numbers. Hope this explains some of the underlying principles surrounding why division of any real number, including zero, by zero is undefined. John John Pickett: N4ES, N600 TI: 58, 30III, 30x Pro MathPrint, 36x Solar, 85, 86, 89T, Voyage 200, Nspire CX II CAS HP: 50g, Prime G2, DM42 

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Messages In This Thread 
Help with problem  levi98  08042019, 06:50 PM
RE: Help with problem  Joe Horn  08052019, 04:24 AM
RE: Help with problem  Aries  08052019, 12:10 PM
RE: Help with problem  Marcel  08052019, 12:32 PM
RE: Help with problem  ijabbott  08052019, 07:19 PM
RE: Help with problem  Han  08062019, 06:26 PM
RE: Help with problem  Marcel  08072019, 12:34 PM
RE: Help with problem  ijabbott  08072019, 01:36 PM
RE: Help with problem  DrD  08072019, 01:17 PM
RE: Help with problem  Marcel  08072019, 05:52 PM
RE: Help with problem  jlind  08102019 10:01 PM
RE: Help with problem  Aries  08122019, 05:58 AM
RE: Help with problem  Tonig00  08132019, 04:36 PM
RE: Help with problem  jlind  08142019, 05:38 AM
RE: Help with problem  Aries  08142019, 06:18 AM

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