# Tagged Questions

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.

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### The Google calculator says that $\left(\frac00\right)^0=1$. Is this true?

According to Google, $\left(\frac00\right)^0=1$. Is this true? Why or why not?
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### Why does simplifying a function give it another limit [duplicate]

I'm asked: $$\lim_{x\to 1} \frac{x^3 - 1}{x^2 + 2x -3}$$ This does obviously not evaluate since the denominator equals $0$. The solution is to: $$\lim_{x\to 1} \frac{(x-1)(x^2+x+1)}{(x-1)(x+3)}$$ ...
2answers
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### How to find slope at a point where the derivative is indeterminate

How should I find the slope of a curve at origin whose derivative at the origin is indeterminate. My original problem is to calculate the equation of tangent to a curve at origin. But for the equation ...
0answers
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### How do I integrate a function with a continuous domain where the integrand is indeterminate ($0.\infty$)?

I have an integral to solve: $$I=\int f\left(g,h\right)~dg = \int_0^1 \theta\left(g-h\right)\log_e\frac{1-h}{\theta\left(g-h\right)}~dg$$ where $\theta()$ is the Heaviside step function, and $h$ is ...
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### Existence and non-singularity of the Fisher information matrix

Consider a random vector $X$ defined on the probability space $(\Omega, \mathcal{F}, \mathbb{P})$, $X: \Omega \rightarrow \mathbb{R}^k$. Suppose $X$ has probability density $p_{\theta_0}$ with respect ...
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### Limit $\lim_{x \to 0} \dfrac{\sin(1-\cos x)}{ x}$

$$\lim_{x \to 0} \dfrac{\sin(1-\cos x)}{ x}$$ What is wrong with this argument: as $x$ approaches zero, both $x$ and $(1-\cos x)$ approaches $0$. So the limit is $1$ . How can we prove that they ...
6answers
153 views

### “Proving” that $0^0 = 1$ [duplicate]

I know that $0^0$ is one of the seven common indeterminate forms of limits, and I found on wikipedia two very simple examples in which one limit equates to 1, and the other to 0. I also saw here: ...
1answer
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### Does symmetric property of Equivalence hold when the left hand side of the equation is in indeterminate form?

The Symmetric Property of Equivalence is a=b implies b=a. This property does not have any conditions on a or b. But what if through manipulation I get $a=\frac00$ where $a$ is a real number does this ...
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### The indeterminacy of 0/0 and vacuous truth?

Today, my roommate and I picked up our friend from the airport. We were supposed to pick him up yesterday, but he missed his flight. We joked that he misses flights a lot, and that only catches 70% of ...
1answer
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### Conventions adopted for extended reals

It is known that $0^0$ despite being an indeterminate limit form, is usually defined to be equal to $1$. I wonder whether similar conventions exist for some other "indeterminate forms" in the context ...
5answers
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### Why does L'Hôpital's rule work for sequences?

Say, for the classic example, $\frac{\log(n)}{n}$, this sequence converges to zero, from applying L'Hôpital's rule. Why does it work in the discrete setting, when the rule is about differentiable ...
2answers
195 views

### Is $\frac00=\infty$? And what is $\frac10$? Are they same? Does it hold true for any constant $a$ in $\frac{a}0$ [duplicate]

I know that $\lim_{x\to0}\frac{x}{x}=$ 1. But in my text book, it is written that it is $\infty$ and even $\frac10=\infty$. But how is it possible? And are they both same? What is the difference ...
3answers
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### Why don't we use undefined forms to find limits of infinity? [closed]

I came across a couple of simple limits of infinity and solved them using the normal subsequence method. Yet, I also tried solving them by substituting the undefined form $\frac{1}{0}$, and although ...
1answer
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### What does it mean for a “formula to be undefined”?

I was covering the techniques used sketch rational functions of five different types as follows: However, then I encountered this: And, Ij just can't find out what it means for the formula to ...
3answers
310 views

### Infinity indeterminate form that L'Hopital's Rule: $\lim_{x\to0^+}\frac{e^{-\frac{1}{x}}}{x^{2}}$

When I tried to find the limit of $$\lim_{x\to0^+}\frac{e^{-\frac{1}{x}}}{x^{2}}$$ by applying L'Hopital's Rule the order of denominator would increase. What else can I do for it?
4answers
80 views

### Undefined reference $1^{\infty}$ in a limit such as $\lim_{n\to\infty}(1+1^n)$ [closed]

If $1^{\infty}$ is undefined reference in a limit, how is $$\lim\limits_{n\to\infty}(1+1^n)=2$$
1answer
47 views