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.

learn more… | top users | synonyms

0
votes
1answer
22 views

limits as $x\rightarrow\pm\infty$ of indeterminate forms $\frac{a^x+b^x}{c^x+d^x}$, where $a,b,c,d\in\mathbb{R}$

Good day sirs would you kindly help me to find the limit of $\frac{a^x+b^x}{c^x+d^x}$ as $x\rightarrow\pm\infty$, where $a$,$b$,$c$ and $d$ are real numbers? I already know how to use the L' ...
4
votes
5answers
681 views

My dilemma about $0^0$ [duplicate]

We know that $0^0$ is indeterminate. But if do this: $$(1+x)^n=(0+(1+x))^n=C(n,0)\cdot ((0)^0)((1+x)^n) + \cdots$$ we get $$(1+x)^n=(0^0)\cdot(1+x)^n$$ So, $0^0$ must be equal to $1$. What is ...
0
votes
0answers
13 views

Limit of an indeterminated form?

I want to find: $$\lim_{t\to\infty}X_{t}$$ where: $$X_{t} = \frac{A_{t}^{a}}{B_{t}}$$ I know that: $$\lim_{t\to\infty}A_{t}=0$$ and $$\lim_{t\to\infty}B_{t}=0$$ Can I say with certainty that: ...
-2
votes
1answer
67 views

What is 0 raised to 0 ???!!!! [duplicate]

I have read many articles on this confusion but i am still confused... My simple question is - What is $0^0$? What is the present agreement to this? I feel that it should be 1 as anything to ...
3
votes
3answers
384 views

Question on using L'Hopital's rule for this problem?

I'm doing some practice questions and I've encountered a wall. The question is: Find the limit of the function $(\ln4x-\ln(x+7))$ as $x \rightarrow \infty$. the indeterminate form is ...
1
vote
3answers
39 views

Determining the indeterminate limit of an exponent problem

I have the equation: $y=\left( 1+\frac{1}{2}^{x} \right)^{x}$ In evaluating it's limit as it approaches +$\infty$, I can't seem to simplify the expression to a non-indeterminate form. By graphing I ...
2
votes
0answers
28 views

Usual and “unusual” indeterminate forms

I've always read there are seven "main" indeterminate forms, 0/0, ∞/∞,∞−∞,0∞,00,1∞,∞0. I've recently started working more keenly on analysis, and the seven "main" forms are never expanded to include ...
2
votes
3answers
47 views

Need help with a limit to infinity involving a radical with indeterminate form (stuck in the factoring)

this is my first time on Math Exchange, I searched around the site and could not find a question for this math problem so I do not believe that I am asking a previously asked question, if I am please ...
2
votes
3answers
56 views

How to evaluate the limit $\lim_\limits{x\to 0+ } \frac{1}{\sqrt{x}}\left ( \frac{1}{\sin x} - \frac{1}{x}\right )$?

$$\lim_{x\to 0^+ } \frac{1}{\sqrt{x}}\left ( \frac{1}{\sin x} - \frac{1}{x}\right ) =\ ?$$ I rearranged it as $$\lim_{x\to 0^+ } \frac{x-\sin x}{x\sqrt{x}\sin x} = \lim_{x\to0^+ } \frac{x-\sin ...
1
vote
2answers
44 views

Indeterminate form as a series

We know that $0 \times \infty$ is an indeterminate form. However, is it equivalent to $0 + 0 + 0 + \cdots$? If yes, why we do not consider $\displaystyle \sum_{n = 0}^\infty 0$ an indeterminate form? ...
2
votes
1answer
34 views

computing an indeterminate form of a limit

I need a hint on computing this one limit: $$\lim_{n \to\infty}\,\frac{2\cdot4^n+3\cdot n^4}{4\cdot n^6-3\cdot 3^n +3n}$$ Thank you
0
votes
1answer
26 views

Limit Problem : Infinity Limit Problem

I can't find the way to solve this question and i always get 0/0. The question is: $\lim_{x\rightarrow \infty } x\left [ 2^{\frac{1}{x}}-1 \right ]$ From Mathematica, i get -infinity. But how can it ...
-1
votes
1answer
73 views

What is the value of 0/0? [duplicate]

I have heard that anything divided by zero is infinity, so i was wondering what would be 0/0? I am a high school student and I haven't studied calculus yet.
0
votes
2answers
88 views

Why Is $1^{\infty}$ an indeteminate form? [duplicate]

For me, multiplication is a binary operation so it can be applied only on a finite sequence of numbers. but $1^{\infty}$ requires that we apply multiplication infinitly which is not defined as ...
0
votes
2answers
48 views

why is $\displaystyle \frac{\log(\sin x)}{\log(x)}$ $\quad\frac{\infty}{\infty}$ form as $x\to 0$?

In this question $\displaystyle\frac{\log(\sin x)}{\log x}$ is taken as $\displaystyle\frac{\infty}{\infty}$ indeterminate form. But $\log(0)$ is not defined so how can L'Hospital's rule can be ...
0
votes
1answer
51 views

Why is this rational expressions indeterminate when evaluated?

I have this rational expression to evaluate, $$ {{3a-3}\over {4a(a-1)}} \text { if } a=1. $$ I understand that if you substitute 1, both the numerator and denominator would turn out 0, thus making ...
3
votes
4answers
256 views

computing a limit of a function that is positive defined

given a function $f(x)$ positive and continuous at $x=a$, with $f(a)\ne0$, compute: $$\lim_{n\to+\infty}\left[\frac{f\left(a+\frac{1}{n}\right)}{f(a)}\right]^n$$ a friend asked me that, though I ...
2
votes
3answers
78 views

indeterminate limit where applying L'Hopitals Rules directly doesn't help and using ln gives wrong answer

I am trying to determine the limit $\displaystyle{ \lim_{x \to 0^-}{\frac{-e^{1/x}}{x}}}$. Plugging in $x$ directly, yields $0/0$ which is indeterminate. Applying L'Hopitals rule does not simplify ...
15
votes
4answers
182 views

I got the answer for $\lim \limits_{x \to \infty} {\left({3x-2 \over3x+4}\right)}^{3x+1}$, but only by a mistake - how do I solve correctly?

This is what I did for: $$\lim \limits_{x \to \infty} {\left({3x-2 \over3x+4}\right)}^{3x+1}$$ Check form: $\left({\infty \over \infty}\right)^{\infty}$. Apply L'Hospital's Rule to just $\lim ...
4
votes
2answers
73 views

Easier way to solve $\lim \limits_{x \to 0} \space \cot{x}-{1 \over x}$ using L'Hospital's Rule?

This is what I did for: $$\lim \limits_{x \to 0} \space \cot{x}-{1 \over x}$$ Check form: $\infty - \infty$. Rearrange it to be a quotient: $$\begin{align} \\ & =\lim \limits_{x \to 0} \space ...
1
vote
0answers
66 views

Is $(-1)^{\infty}$ an indeterminate form?

We know that $\lim_{n\to\infty}(-1)^n=(-1)^{\infty}$ doesn't exist. Now take $\lim_{n\to\infty}(-1)^{2n}=(-1)^{\infty}$. This limit exists, because ...
1
vote
1answer
105 views

Determination of $1^\infty$ indeterminate forms

Recently I have been learning some of the basic concepts of limits and in my academics. There I have been taught some methods to evaluate indeterminant forms like $1^\infty$, $0^0$ and $\infty^0$. ...
1
vote
2answers
74 views

How to explain indeterminations, and some aprpoaches to $+\infty$ or $-\infty$, for middle school students?

Question: how to explain the undefinitions $0^0$ and $\frac{0}{0}$ for Middle school students?? I am a math teacher and I don't know how to answer properly when studens ask me why some operations ...
2
votes
3answers
135 views

Using L'Hospital's Rule to evaluate limit to infinity

I'm given this problem and I'm not sure how to solve it. I was only ever given one example in class on using L'Hospital's rule like this, but it is very different from this particular problem. Can ...
0
votes
1answer
76 views

Help me integrate this function using Simpson's rule

I have a question: compute $$\int_0^1 \frac{\sin(x)}{x}\,dx$$ for $n=10$ divisions. I got the value $0.9127$ but I think its a bit too high.
4
votes
2answers
84 views

Why can $2^3$ be defined but $0^0$ cannot

From what I gather, we can't just define $0^0$ to be $0$ or $1$ or $69$ or whatever, because $\lim\limits_{x\mathop\to0}0^x=0$ and $\lim\limits_{x\mathop\to0}x^0=1$. So $0^0$ is called indeterminate ...
0
votes
1answer
296 views

Limits of Indeterminate Powers in Exponential Form using L'Hopital's Rule

I am trying to find the limit as $x \rightarrow 0$ of $x^x$ using L'Hopital's rule. I have written it in exponential form: $\lim\limits_{x \rightarrow 0} e^{x \ln x}$. I do not know how to put it in ...
2
votes
3answers
42 views

Limit of a polynomic-exponential sequence

I have to calculate the following limit: $$L=\lim \limits_{n \to \infty} -(n-n^{n/(1+n)})$$ I get the indeterminate form $\infty - \infty$ and I don't know how to follow. Any idea? Thank you very ...
2
votes
3answers
174 views

Indeterminate limit that is supposed to be solved with De L'Hospital's rule

Last week my Maths teacher gave the class this exercise taken from our text book. We are working on De L'Hospital's rule at the moment and this exercise is from that part of the book so everybody ...
0
votes
1answer
35 views

Is zero a singular point of this function?

$$f(z)=\frac{z^3}{z+z^5}$$I thought that this function has 5 singular points. But my friend is convinced it only has four because if you write is as$$f(z)=\frac{z^2}{1+z^4}$$ then it is defined at ...
1
vote
3answers
301 views

Solving limit without L'Hopital

I'd like some help in solving this limit without using L'Hopital. $$\lim_{x\to -\infty}\frac{\ln(1-2x)}{1-\sqrt{1-x}}$$ I've also solved it changing the variable to $y=\sqrt{1-x}$ but I would like ...
1
vote
3answers
172 views

Is $\frac{0}{\infty}$ indeterminate?

I have been searching for an answer for this for half an hour and I can't seem to find one. I've lots of information about other combinations of $0$ and $\infty$ but I haven't seen anything that says ...
42
votes
12answers
5k views

Is it wrong to tell children that $1/0 =$ NaN is incorrect, and should be $∞$?

I was on the tube and overheard a dad questioning his kids about maths. The children were probably about 11 or 12 years old. After several more mundane questions he asked his daughter what $1/0$ ...