when a limit equals zero over zero what does that represent ?

Question

when we substitute in limits and get these answers,
what does it represent when the limit equals:
zero over zero e.g. lim x>5= 0/0
Non_zero over zero e.g. limx>5= 8/0
Zero over non zero e.g. lim x>5= 0/77

Do we have limit ?

Answer 1

When computing limits, if you get 0/0, you have to do more work! The limit in this case may turn out to be anything! That is why it is called an indeterminant limit,

If you get 8/0, the limit will not exist because it will go to infinity.

If you get 0/77, the limit is 0.

Answer 2

well you cannot divide by 0 so both the first and second would not be right, but the fact that you get 0 on the bottom does not mean that the limit does not exist.
e.g. lim x>5 (x^2-7x+10)/(x-5) if you substitute 5 in now, you would get 0/0, but that is not right
In this equation you can factor out an (x-5) and you get
lim x>5 (x-2) meaning the limit is 3

There is usual a way to manipulate the equation so that you do not get a 0 in the denominator, so you can do that for the nonzero over zero equation.

When you have 0/77 the limit is just 0. You can divide 0 by something, but you can't divide something by zero.

Answer 3

Limits Zero Over Zero

Answer 4

Limits of the form 0/0 are indeterminate, and may or may not exist -- if they exist, they may be ∞, -∞, or any real number. In order to evaluate limits of this form, individual consideration of each function is required. Common strategies include (but are not limited to) cancellation of terms and the use of L'hopital's rule.

Limits of the form n/0 where n≠0 are always either infinite or nonexistent -- they cannot be equal to any real number. To determine what the limit is, consider the sign of the denominator -- if it is always positive in some punctured neighborhood of the point the limit is being evaluated at (which we'll call c), then the limit is ∞ if n is positive and -∞ if n is negative. Conversely, if the denominator is always negative in some punctured neighborhood of c, the limit is -∞ if n is positive and ∞ if n is negative. Finally, if the denominator attains both positive and negative values in every neighborhood of c, the limit does not exist, because the function oscillates between positive and negative values.

The case of 0/n where n≠0 is extremely simple -- such limits are always equal to 0. It's just the same as if it were any other number over a nonzero denominator.

Answer 5

Hmm... Well, limits is NOT substituting zeros into the equation when limits TENDS to be zero!
0/0 means that there is no limit, the limit is undefined. Same is the case with 8/0.
0/77 means that it is 0.
I think you should look at the equations and try other methods of FINDING limits. Limits is NOT just evaluating of the equation for a particular number.
Hope this helps!

Answer 6

if you calculate a limit and it turns out to be zero/zero then that is considered an indeterminate form and you need to apply L'Hopitals rule to calculate the limit. Basically you take the derivitive of the numerator and the derivitive of the denominator and try again to calculate a limit.

nonzero/zero implies that a limit does not exist...the function increases without bound as you approach the limit point.

zero/nonzero is well defined...the limit is zero

Answer 7

If you get 0/0, it means you don't have the limit yet. Some technique is needed, one being L'Hospital's Rule. If you haven't learned L'Hospital's Rule yet, you will soon.

a/0, a ≠ 0, points to an unbounded limit, i.e. limit = ∞

0/a, a ≠ 0 means the limit is zero.