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Subject: "Some questions on Caculus"     Previous Topic | Next Topic
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Lei You
guest
 Oct-09-02, 08:14 AM (EST)
 
"Some questions on Caculus"
 
   0
---
0

is there such a mathematical symbol? ( 0 / 0 )

(0 / 0) / dx = 1 / x ?

or

dx / (0 / 0) = x ?

can we have ddx ?


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alexb
Charter Member
856 posts		 Oct-10-02, 10:20 PM (EST)
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1. "RE: Some questions on Caculus"
In response to message #0
 
   > 0
>---
> 0
>
>is there such a mathematical symbol? ( 0 / 0 )

What do you mean by "is there"? And what do you mean by the word "symbol"?

You can of course write "0/0" and ponder its meaning. Would it'symbolize anything? Yes, of course. It would symbolize a quandary people have been asking in droves. Does it symbolize any definite quantity - finite or infinite? Usually it does not. Not in the context of Calculus. But in some engineering problems I heard it is convenient to assign to 0/0 the value of 1.

>(0 / 0) / dx = 1 / x ?

Have no idea what you mean here. What is dx?

>dx / (0 / 0) = x ?
>
>can we have ddx ?

Depends on what yo mean by dx.


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Lei You
guest
 Oct-13-02, 08:28 AM (EST)
 
2. "RE: Some questions on Caculus"
In response to message #1
 
   i was fiddling around with implicit differentiation the other day.

d (x^n) can be rewritten as
n / b * x ^ (n-b) * d(x^b),
where b is constant

so if b = 1, n = 2

d (x^2)
= x ^ (2-1) * d(2*x^1/1)
= x * d(2x)
= 2x * d(x)

but, what if b = 0

the RHS expression then becomes

n/0 * x^n d(x^0)

then d(x^0) = 0, since x^0 is a constant 1

i.e

d(x^n) = n*x^n * (0 / 0)

but

d(x^n) / dx = n*x^(n-1)

the RHS is n*x^n * (0/0)

i.e

n*x^n * (0/0) / dx = n*x^(n-1)

i.e

(0/0) / dx = 1 / x

dx / x = ? (0 / 0)?


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