Note that all of the standard examples where it's "convenient" to have $0^0=1$ (e.g. power series) are all ...

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2015年1月12日 · Most introductory calculus texts have a section on the problems with $0^0$, because it leads to some of the more common mistakes (from my experiences teaching calculus, anyway). For example, $\lim_{x\to 0^+} e^{-1/x} = 0$ and $\lim_{x\to 0^+} x = 0$, but $\lim_{x\to 0^+} (e^{-1/x})^x \neq 1$. $\endgroup$ –

2018年7月4日 · $\begingroup$ In Apostol's Introduction to Analytic Number Theory he states that $0^0=1$. Also for $0!=1$, you should check the Gamma function, which extends the factorial function and has $\Gamma(1)=0!=1$. $\endgroup$ –

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2018年6月27日 · when I try to show that the derivative of exp function is $$\frac{\partial e^t}{\partial t}=e^t$$ I need to prove firstly that this limit is equal to 1. $$\lim_{h\to 0} \, \frac{e^h-1}{h}=1$$ If you try to use L'Hospital's rule then you need firstly to know what is the derivative of exp function that we want to prove it.

2014年12月16日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

I was messing around with the definition of the derivative, trying to work out the formulas for the common functions using limits. I hit a roadblock, however, while trying to find the derivative of...