# 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.

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### Evaluating $\lim_{x\to0}\,3^{(1-\sec^220x)/(\sec^210x-1)}$

I want to evaluate $$\lim_{x\to0}\;3^{(1-\sec^220x)/(\sec^210x-1)}$$ So far these have been my ideas, feel free to correct me: Find that if directly applied to the function, $x_0$ will cause ...
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1 vote
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### $\lim_{x\to \infty} (x^4 +5x^3+3)^c-x=k$. Find $k$ and $c$.

$\lim_{x\to \infty} (x^4 +5x^3+3)^c-x=k$. Find $k$ and $c$. key points: This is supposed to be solved with knowledge of just L'hospital's rule. *The value of limit i.e, k is finite and non zero I ...
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1 vote
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### calculating $\lim\limits _{x\to0}\left(\frac{1}{x^{2}}-\frac{e^{x}}{\left(e^{x}-1\right)^{2}}\right)$ using taylor polynomials

I am trying to calculate the limit $$\lim\limits _{x\to0}\left(\frac{1}{x^{2}}-\frac{e^{x}}{\left(e^{x}-1\right)^{2}}\right)$$ using taylor polynomials. I tried using L'Hôpital's rule, but it was ...
• 271
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### Why is $0/\lim_{x\to0} x$ undefined, when $\lim_{x\to2} (x^2-4)/(x-2)$ is defined?

For $\lim\limits_{x\to2}\ (x^2-4)/(x-2)$, we are able to cancel out $x-2$ and rewrite it as $\lim\limits_{x\to2} x+2$ But in maths, we are not able to cancel out $0$ values so $x-2$ is not zero, and ...
• 11
1 vote
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### $0^\infty$ and indeterminate forms

I have actually two related questions: 1. Should indeterminate forms be able to attain an infinite number of values to be considered indeterminate? I’m asking because Wikipedia says: The expression 1/...
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### How to prove that a form like $0^\infty$ is not an indeterminate form? What makes a form indeterminate?

I just wanted to know why some particular forms (seven of them) are called indeterminate forms. Why are there only seven indeterminate forms? Can anyone please prove why $0^\infty$ is not an ...
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### Can we apply L'hopital Rule when we have $\frac{-\infty}{+\infty}$?

I saw in a book, it evaluated $\lim_{x\to0^+}\cfrac{(\ln x)^3}{\frac1x}$ with L'hopital Rule. the fraction is $\frac{-\infty}{+\infty}$ actually. so can I use L'hopital rule safely every time I see ...
• 5,575
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### Infinity as a limit in an indeterminate form

There is this limit $$\lim_{x\to1}\frac{\ln x}{\left(x-1\right)^{2}}$$ for which I built a graph and I know the answer, so the question is not about how to compute it, but about my observation that ...
• 922
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### Is it logical to say that $2\over 0$ $\ne$ $2\over 0$?

As I was doing a math exercice, I came across a question which I decided to prove by contrapositive. That required me to show that $f(4-x)$ $\ne$ $f(x)$ - but in both cases the result was $2\over 0$....
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### Restrictions on laws

I'm wondering about the restrictions, my doubt is for example at $\log_a(b)=c\implies a^c=b$, how would anyone add the restrictions for this? I know the argument and the base of a log have to be >0 ...
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### verifying $\lim\limits_{x \to \infty} (1+\frac{1}{\sqrt{x}})^x$
What is the limit of $\lim\limits_{x \to \infty} (1+\frac{1}{\sqrt{x}})^x$ ? I tried to solve it but I am not sure if it is appropriate to solve it this way. \$(1+\frac{1}{\sqrt{x}})^x =\exp\Bigl({x\...