2008-11-15, 10:34 PM
So after reading through this all I can say is... missed the point much? Sure you guys explained why 1^inf isn't defined but that doesn't technically answer the original question. You never explained why it isn't 1.
Here's your answer OP:
The reason 1^inf isn't defined is because in calculus, limits involving said situation are... well, I'll just show you:
lim x->0 (1+x)^ 1/x
If you straight out plug in zero, you're looking at a situation of 1^inf. You'd think that the answer to this is 1 right?
However,
lim x->0 (1+x)^ 1/x = e ~ 2.71828
Conclusively it can also take on any other number of answers:
ex. 1
lim x->0 (1+x)^ ln 5/x
Once again plugging in 0 gives you another 1^inf situation.
However the answer is 5.
ex.2
in general
lim x->0 (1+x) ^ k/x = e^k
So as you can see, the reason it isn't 1 is because of situations like these. You can make a 1^inf situation give you any positive answer you want.
I hope this answered your question Russt.
P.S. I didn't mean to sound as if the rest of you guys didn't give the right answer. You technically did, but just in the wrong way. While it gave the explanation as to why 1^inf wasn't defined, you didn't say why it wasn't 1 when it looks like it should be 1.
Here's your answer OP:
The reason 1^inf isn't defined is because in calculus, limits involving said situation are... well, I'll just show you:
lim x->0 (1+x)^ 1/x
If you straight out plug in zero, you're looking at a situation of 1^inf. You'd think that the answer to this is 1 right?
However,
lim x->0 (1+x)^ 1/x = e ~ 2.71828
Conclusively it can also take on any other number of answers:
ex. 1
lim x->0 (1+x)^ ln 5/x
Once again plugging in 0 gives you another 1^inf situation.
However the answer is 5.
ex.2
in general
lim x->0 (1+x) ^ k/x = e^k
So as you can see, the reason it isn't 1 is because of situations like these. You can make a 1^inf situation give you any positive answer you want.
I hope this answered your question Russt.
P.S. I didn't mean to sound as if the rest of you guys didn't give the right answer. You technically did, but just in the wrong way. While it gave the explanation as to why 1^inf wasn't defined, you didn't say why it wasn't 1 when it looks like it should be 1.