Help with problem

08042019, 06:50 PM
Post: #1




Help with problem
Using hp prime need help 

08052019, 04:24 AM
Post: #2




RE: Help with problem
In CAS: domain((x5)/(x^225)) > x≠5 AND x≠5
<0ɸ0> Joe 

08052019, 12:10 PM
Post: #3




RE: Help with problem  
08052019, 12:32 PM
Post: #4




RE: Help with problem
Hi!
For myself I prefert to do a simplification before using de domain function! After that, the domain is OK… Choice A with 5. Marcel 

08052019, 07:19 PM
Post: #5




RE: Help with problem
(08052019 12:32 PM)Marcel Wrote: Hi! Technically, doesn't simplifying \(\frac{x5}{x^225}\) to \(\frac{1}{x+5}\) change the domain? I know the original approaches \(\frac{1}{10}\) in the limit as \(x \to 5\), but it should probably have an open circle at \((5, \frac{1}{10})\). — Ian Abbott 

08062019, 06:26 PM
Post: #6




RE: Help with problem
(08052019 12:32 PM)Marcel Wrote: Hi! Unfortunately, "simplifying" here is actually division, whereby \( x5 \) in both the numerator and denominator would divide each other out EXCEPT when \( x=5 \) because this would lead to division by 0. Graph 3D  QPI  SolveSys 

08072019, 12:34 PM
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RE: Help with problem  
08072019, 01:17 PM
(This post was last modified: 08072019 01:28 PM by DrD.)
Post: #8




RE: Help with problem  
08072019, 01:36 PM
Post: #9




RE: Help with problem
(08072019 12:34 PM)Marcel Wrote: Hi! Maybe this helps? 2.7 Holes in Rational Functions. — Ian Abbott 

08072019, 05:52 PM
Post: #10




RE: Help with problem
Hi ijabbott!
Thank you, this is clear now. Marcel. 

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 Calculators: Pickett: N4ES, N600 TI: 58, 30III, 36x, 85, 86, 89T, Voyage 200, Nspire CXii CAS HP: 50g, Prime G2 (rev D), DM42 

08122019, 05:58 AM
Post: #12




RE: Help with problem
There is one vertical asymptote (x=5) and y=0 (i.e. xaxis) is the horizontal asymptote.
There is no slant asymptote. Best, Aries 

08132019, 04:36 PM
Post: #13




RE: Help with problem
I would likevto point out that is clearvthat 0/0 is undefined.
But any real number>0 divided by 0 I would say is infinite. When we have a function in single variable I would say that if left an right limits are the same, then it is definite. It may be the case of for example 5/(x5)^2. 

08142019, 05:38 AM
(This post was last modified: 08142019 05:40 AM by jlind.)
Post: #14




RE: Help with problem
(08132019 04:36 PM)Tonig00 Wrote: I would likevto point out that is clearvthat 0/0 is undefined. Tonig00, Any number, divided by zero, is undefined.
Let 1 = x Multiply by x to get x = x^2 Subtract 1 from each side to get x  1 = x^2  1 Divide both sides by x − 1 (this is a hidden division by zero as x = 1) (x  1) / (x  1) = (x^2  1) / (x  1) 1 = ((x  1) * (x + 1)) / (x1) which simplifies to 1 = x + 1 Since x = 1, by substitution: 1 = 1 + 1, and therefore: 1 = 2 This is impossible. Hope this helps some with understanding why any number divided by zero is undefined. John John Calculators: Pickett: N4ES, N600 TI: 58, 30III, 36x, 85, 86, 89T, Voyage 200, Nspire CXii CAS HP: 50g, Prime G2 (rev D), DM42 

08142019, 06:18 AM
Post: #15




RE: Help with problem
(08132019 04:36 PM)Tonig00 Wrote: I would likevto point out that is clearvthat 0/0 is undefined. I'd say 0/0 is indeterminate (form), taking limit into account. Best, Aries 

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