Zero Divided By Zero

[nycmathguy]

I know that we cannot divide by zero.

Let x = any number.

I know that x/0 = undefined.

I know 0/0 is not 0. It is called indeterminate.

1. What does indeterminate mean?

2. What makes 0/0 indeterminate?

3. If zero is a number (and it is), then why is 0/0 not equal 1?

 

[MathLover1]

1. 0/0 is undefined or indeterminate (which means not exactly known, established, or defined)
2. What makes 0/0 indeterminate?-> division by 0
3. If zero is a number (and it is), then why is 0/0 not equal 1?-> because division by 0

 

[nycmathguy]

1. 0/0 is undefined or indeterminate (which means not exactly known, established, or defined)
2. What makes 0/0 indeterminate?-> division by 0
3. If zero is a number (and it is), then why is 0/0 not equal 1?-> because division by 0

Is the idea of 0/0 discussed in calculus 1 or 2?
What is the calculus definition of 0/0?

 

[MathLover1]

the calculus definition: if the limit is =0/0, since 0/0 is an indeterminate form, the limit may (or may not) exist
lim(x→4,(2x+1)/(x(x−4))=(2(4)+1)/(4(4−4))=9/0 =>the limit does not exist
lim(x→0,(ln(x)/(1/x))=0=>the limit does exist
If you are dealing with limits, then 0^0 is an indeterminate form, but if you are dealing with ordinary algebra, then 0^0 = 1.

 

[nycmathguy]

the calculus definition: if the limit is =0/0, since 0/0 is an indeterminate form, the limit may (or may not) exist
lim(x→4,(2x+1)/(x(x−4))=(2(4)+1)/(4(4−4))=9/0 =>the limit does not exist
lim(x→0,(ln(x)/(1/x))=0=>the limit does exist
If you are dealing with limits, then 0^0 is an indeterminate form, but if you are dealing with ordinary algebra, then 0^0 = 1.

Question:

When we get 0/0 in Calculus 1 or 2, does L'Hospital's Rule apply?

 

[MathLover1]

you start with computing limits in Calculus 1
L'Hospital's Rule works great on the two indeterminate forms 0/0 and ±∞/±∞.

 

[nycmathguy]

you start with computing limits in Calculus 1
L'Hospital's Rule works great on the two indeterminate forms 0/0 and ±∞/±∞.

I can't wait to begin my calculus studies. I want to complete the Ron Larson Precalculus journey first. I got an A minus in Precalculus at Lehman College but this was in 1993. Long time ago.