| Author | Comment |
retsia
Probe
Posted: 22 Dec 2005
15:57 GMT
Total Posts: 3 | From Calculus
I may have found a flaw in the TI-83+ calculators as well as more advanced graphing calculators.
the theorem is:
(1+(1/x))^x where this equals to e or approximately 2.7. Really, you can insert anything for "x"...it will equal 2.7. However, that is not the case with 83+ calculators...when I insert 10000000000000000000 as "x" I get 1 as the answer. Can you tell me how that happens? |
Andy
Administrator
Posted: 22 Dec 2005
18:38 GMT
Total Posts: 939 | It's a precision problem. The calculator can only hold so many digits of a number, and as you run x off towards infinity, it can't store enough information so it will eventually return 1. It's just fine for the first several powers of ten. |
Lunchbox
Carrier
Posted: 23 Dec 2005
08:26 GMT
Total Posts: 2007 | If you calculate the limit as the equation approaches infinity, you will find it is equal to e.
[Edited by Lunchbox on 23-Dec-05 17:26] |
Andy
Administrator
Posted: 23 Dec 2005
17:21 GMT
Total Posts: 939 | But not on the calculator, that's my point. |
retsia
Probe
Posted: 23 Dec 2005
21:08 GMT
Total Posts: 3 | See...I see it as a weakness problem from the aspect of TI calculators. I do not wish the calculator to approach infinity (that would be absurd), but to calculate to mere 10^18, a miniscule fraction of infinity. Quite frankly, I am disappointed by TI products (not just 83+). But I shouldn't brag about it...it is not a professional tool and, I guess, if I wanted 10^18, I would need a powerful computer, or program. But still... |
Lunchbox
Carrier
Posted: 24 Dec 2005
08:23 GMT
Total Posts: 2007 | There is a formula for calculating limits without going through the whole sequeence, so you can use that and have the number go up to 10^99 |
Andy
Administrator
Posted: 24 Dec 2005
14:11 GMT
Total Posts: 939 | 10^18 is pretty damn big from the point of view of what the calculator can hold. By itself it's fine, but if you reciprocate it, then it's infintessimal, which the calculator canNOT handle as easily.
This is a prime example of why you have to PAY ATTENTION in class and not rely on the calculator alone; knowledge is important! |
jessef
Goliath
Posted: 24 Dec 2005
19:57 GMT
Total Posts: 192 | I do not wish the calculator to approach infinity (that would be absurd),
absurd as it sounds limits of infinity are very important in calculus |
retsia
Probe
Posted: 27 Dec 2005
12:10 GMT
Total Posts: 3 | Lol! Do you guys understand English or are you all that empty-clever to state irrelevant statements just for the hell of it. I know that infinity is important in Calculus from integrals (finding an area underaa curve) to derivatives and so on. If you look more closely at my simple statement you will discover that I was speaking from the perspective of the calculator. IT cannot apporach infinity from its purposeful limitations! |
Andy
Administrator
Posted: 27 Dec 2005
19:37 GMT
Total Posts: 939 | And you are misunderstanding that it CAN and DOES approach infinity in terms of how it stores numbers. (Or rather, 1/infinity)
[Edited by Andy on 28-Dec-05 04:38] |
BullFrog
Wraith
Posted: 27 Dec 2005
20:55 GMT
Total Posts: 623 | I believe your problem lies in the Order of Operations.
If I recall correctly, the calculator will work from the inside out in this case. Therefore, it will analyze 1/x first. Now, 1/10000000000000000000 is essentially zero for our purposes.
So we now basically have 1^10000000000000000000. One to almost anything is just one. (I can't remember if infinity is an exception...)
Does anyone else concur or am I just a raving lunatic right now?
[Edited by BullFrog on 28-Dec-05 05:57]
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"Men are not prisoners of fate, but only prisoners of their own minds." -Franklin D. Roosevelt |
