Mathematics Stack Exchange
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Questions tagged [indeterminate-forms]

If the expression obtained after any substitution during limit analysis does not give enough information to determine the original limit, it is known as an indeterminate form.

A mathematical expression can said to be indeterminate if it is not definitively or precisely determined. Certain forms of limits are said to be indeterminate when merely knowing the limiting behavior of individual parts of the expression is not sufficient to actually determine the overall limit.

Basically there are seven form of indeterminate 0 × ∞, 0/0, ∞0, ∞ − ∞, 1∞, 00 and ∞/∞.

368 questions
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Justifying why 0/0 is indeterminate and 1/0 is undefined

$\dfrac 00=x$ $0x=0$ $x$ can be any value, therefore $\dfrac 00$ can be any value, and is indeterminate. $\dfrac 10=x$ $0x=1$ There is no such $x$ that satisfies the above, therefore $\dfrac 10$ is undefined. Is this a reasonable or naive…
helpme
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How should indeterminate be depicted on a Cartesian plane?

I've got a student in a senior year maths class, who is adamant that it is incorrect to depict it as a hole, even though this is the standard way of depicting it. I couldn't find any problems with his reasoning. So I've asked him to put his…
H Borrow
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Can we say that $\frac{0}{0}$ is every number?

Suppose we have an equation $ab=0$. This equation is true when statements $a=0$ or $b=0$ are true. If $a=0$, then $b=\frac{0}{0}$. That means $b$ could be any number for $ab=0$ to be true. If the set which groups all the numbers is the complex set,…
Garmekain
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What is undefined times zero?

Einstein's energy equation (after substituting the equation of relativistic momentum) takes this form: $$E = \frac{1}{{\sqrt {1 - {v^2}/{c^2}} }}{m_0}{c^2} % $$ Now if you apply this form to a photon (I know this is controversial, in fact I would…
Sierra
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For basic operations is it valid that once indeterminate always indeterminate?

For the basic math operations addition, subtraction, multiplication, fractions and negate using integers is the following always true, If any part of an operation is indeterminate the result is indeterminate? TL;DR I am creating a symbolic math…
Guy Coder
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If 0 / 0 is indeterminate, are all clauses "0 / 0 != x" true

Elsewhere arose a discussion about logical clauses that can be made from indeterminate forms, in this case, namely $0 / 0$. Since $0 / 0$ is indeterminate form, can we make these logical clauses: $0 / 0 = 1$ is false? $0 / 0 \neq 1$ is true? Or in…
Elmo Allén
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Are $\log_1 1$ and $\log_0 0$ indeterminate forms?

Are $\log_1 1$ and $\log_0 0$ indeterminate forms? Whenever I ask someone about these indeterminate forms, they deny by saying either $\log$ is neither defined at base $0$ nor at base $1$, or they say $\log$ is a function so these must not be…
PranshuKhandal
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Though $0^0$ is an indeterminate form of limits, is it undefined?

I’ve done a my research, though I have not been able to find an adequate explanation as to whether or not $$0^0$$ exists as a real number, and why or why not? I must credit this question to “Question on the controversial ‘undefined’ $0^0$.” This…
gen-ℤ ready to perish
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Is $\dfrac{0}{0}$ indeterminate with respect to limit only or in general?

Is $\dfrac{0}{0}$ indeterminate with respect to limit only like $\lim_{x\to 0}\dfrac{\sin x}{x}$ or it is indeterminate in general like $\log_1 1$? I asked this because I encountered indeterminates only in limits, we don't talk about in other…
user3290550
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Is $\lim_{x \to a} \sqrt[K(x)]{L(x)},$ indeterminate, where $\lim_{x \to a} K(x)=\infty, \lim_{x \to a} L(x)=\infty$?

Is $\lim_{x \to a} \sqrt[K(x)]{L(x)},$ indeterminate, where $\lim_{x \to a} K(x)=\infty, \lim_{x \to a} L(x)=\infty$? I do not know how one would show that this is true or otherwise.
Jack Pan
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Indeterminate forms

Is $\dfrac{1}{\frac{0}{0}-1}$ an indeterminate form? I thought only $\dfrac 00,\,\dfrac\infty\infty$ and any form that can be represented in those two are indeterminate. Moreover, how do we know if a form is indeterminate? P.S. For people who says…
mathnoob123
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indeterminate forms; definition

$\lim_{x\to 0} \frac{x}{x}$ is an indeterminate form whereas $\lim_{x\to 0} \frac{[x^2]}{x^2}$ is not an interminate form (where $[x]$ represents the greatest integer function Why is $\lim_{x\to 0} \frac{[x^2]}{x^2}$ not in indeterminate…
Yashas
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Is $\frac{0}{0}$ a set?

Say we want to find a number $x$ such that: $$x^2-5x+6=0$$ So, there's no unique value of $x$ satisfying that but we still say $x={2,3}$ Is the situation with $\frac{0}{0}$ the same? I mean, finding the solution of $x\cdot 0=0$. And, since all…
user402662
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Indeterminate form and equality of expressions.

Given this chain of equalities: $$\frac{\sqrt{1-x} - \sqrt{1+x}}{x}=\frac{(\sqrt{1-x} - \sqrt{1+x})(\sqrt{1-x} + \sqrt{1+x})}{x(\sqrt{1-x} + \sqrt{1+x})} = \frac{(\sqrt{1-x})^2 - (\sqrt{1+x})^2}{x(\sqrt{1-x} + \sqrt{1+x})} = \frac{(1-x) -…
user3195997
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Indeterminate forms and l'Hospital rule

The graph of a function and its tangent line at $0$ are shown in image. What is the value of $\lim_{x \to 0} \frac{f(x)}{e^x-1}$?
Urmil aka Vicky
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