Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

please what are the answers and proofs to the following questions

e raised to the power 1 (e^1)

e raised to the power infinity (e^infinity)

e raised to the power of minus infinity (e^-infinity)

0 raised to the power infinity (0^infinity)

0 raised to the power -infinity (0^-infinity)

any number like 2 or 3 raised to the power of plus infinity or minus infinity

share|improve this question

closed as off-topic by Thursday, RecklessReckoner, Tomás, Potato, Hakim Jul 19 at 23:23

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Thursday, RecklessReckoner, Tomás, Potato, Hakim
If this question can be reworded to fit the rules in the help center, please edit the question.

3  
Welcome to math.SE: since you're new, I wanted to let you know few things about the site. Titles should be informative. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. –  user2468 Aug 28 '12 at 0:28
    
Point no. 3 in the answer has one small mistake - its x to the power -n. –  user66721 Mar 14 '13 at 11:49

1 Answer 1

Remark 1: You should care more about the quality of your question.

Remark 2: There are more rigorous argument for some of these, but I stress on the intuition since you seem clueless. For more information you should read in the Wikipedia page on exponentiation and the math.SE post titled any number raised to the power of infinity and related post titled Negative 1 to the power of Infinity.

  1. $e^1 = e$. For all $x$ we have $x^1 = x.$

  2. $e^{\infty} = \infty$. For all $x > 1$ we have $\lim\limits_{n \to \infty} x^n = \infty$. Think of it in terms of a simple example $2^1,$ $2^2,$ $2^3,$ and so on. It gets bigger and bigger.

  3. $e^{-\infty} = \dfrac{1}{e^\infty} = 0$. For all $0 < x < 1$ we have $\lim\limits_{n \to \infty} x^{n} = 0$. Think of it in terms of a simple example $\frac{1}{2^1}=\frac{1}{2},$ $\frac{1}{2^2}=\frac{1}{4},$ $\frac{1}{2^3}=\frac{1}{8},$ and so on. It gets smaller and smaller.

  4. $2^{\pm \infty}$ and $3^{\pm \infty}$ are just similar to $e^{\pm \infty}$.

  5. $0^\infty = 0$. No matter how many times you multiply $0$ together, you'll get $0$.

  6. $0^{-\infty}$ is undefined. For all $x$ we have $x^{-n} = \dfrac{1}{x^n}$. For all $n > 0$ we have $0^n = 0$. And finally $\dfrac{1}{0}$ is undefined. So putting it together: $0^{-\infty} = \dfrac{1}{0^\infty} = \dfrac{1}{0} = \text{undefined}$.

share|improve this answer

protected by Zev Chonoles Jun 22 '13 at 16:14

Thank you for your interest in this question. Because it has attracted low-quality answers, posting an answer now requires 10 reputation on this site.

Would you like to answer one of these unanswered questions instead?

Not the answer you're looking for? Browse other questions tagged or ask your own question.