Why is 0 0 indeterminate and not undefined?

Division requires multiplying by a multiplicative inverse, and 0 doesn’t have one. Those expressions are about limits, not about numbers. We say that 00 is an indeterminate form because a limit of that form can take any value:limy→0xyy=x, for any real number x.

What does it mean for 0 0 to be indeterminate?

When calculus books state that 00 is an indeterminate form, they mean that there are functions f(x) and g(x) such that f(x) approaches 0 and g(x) approaches 0 as x approaches 0, and that one must evaluate the limit of [f(x)]g(x) as x approaches 0. In fact, 00 = 1!

Is undefined over 0 indeterminate?

Originally Answered: What’s the difference between undefined and indeterminate? ‘Undefined’ does NOT have a value or its just not defined. ‘Indeterminate’ has a value which cannot be precisely known. value of a real number divided by zero is undefined, in geometry definition of line, point,plane are not defined.

Is indeterminate the same as undefined?

The big difference between undefined and indeterminate is the relationship between zero and infinity. When something is undefined, this means that there are no solutions. However, when something in indeterminate, this means that there are infinitely many solutions to the question.

Is the limit of 0 1 an indeterminate form?

0/0 is the name for that case, and it’s a special case because it has special techniques that work for it, while other indeterminate forms might not; 1/0 is an undefined number but it isn’t an indeterminate form of the limit; that’s a limit that goes infinite; the limit doesn’t approach a number.

Is zero also undefined?

We can say that zero over zero equals “undefined.” And of course, last but not least, that we’re a lot of times faced with, is 1 divided by zero, which is still undefined.

Why is Infinity 0 indeterminate?

When you divide infinity by 0, we don’t know whether you’re dividing by a positive or negative number, so we can’t determine if the result is infinity or negative infinity. That’s why it’s indeterminate.

What’s the difference between 0 and undefined?

1.An undefined slope is characterized by a vertical line while a zero slope has a horizontal line. 2. The undefined slope has a zero as the denominator while the zero slope has a difference of zero as a numerator.

Is undefined and indeterminate form?

An undefined expression involving some operation between two quantities is called a determinate form if it evaluates to a single number value or infinity. An undefined expression involving some operation between two quantities is called an indeterminate form if it does not evaluate to a single number value or infinity.

Why is 0/0 indeterminate and not 1/0?

The exact form 0/0 is not defined because division by zero doesn’t exist. The limiting form 0/0 is indeterminate because it could be anything. 1/0 is not undefined. It doesn’t even exist. If 1 0 = undefined, 0 × undefined would be 1, but that’s not the case as undefined times anything remains undefined.

Why is the limit of 0/0 undefined?

Because you can’t divide by zero. However, the limiting form of 0/0 is not undefined. In calculus, 0/0 is an indeterminate form. That means you can’t determinate the limit or even know whether it exists or not. Luckily, you can use L’Hopital’s rule when evaluating 0/0 limits.

Why does 0^0 evaluate to 1 when x^2 is undefined?

For several reasons, the expression 0^0 is generally understood to evaluate to 1, even though (in limits) this is an indeterminate form, because as x -> 0, 0^ (x^2) -> 0 and x^0 -> 1. Of course, a function with a “removable discontinuity” is undefined at the point in question even if the limit does not have an indeterminate form.

What is the difference between indeterminate form and undefined form?

Doctor Vogler replied: The phrase “indeterminate form” is used in the context of limits, whereas “undefined” refers to evaluating functions, and “no solution” refers to solving equations or similar problems. Let’s look at some examples from each of these different contexts.