Question Number 130607 by Study last updated on 27/Jan/21
$$\infty^{\infty} =? \\ $$
Commented by MJS_new last updated on 27/Jan/21
![∞^∞ =? (1 question mark! ⇒ easy!!) 0^0 =?? (2 question marks!!! ⇒ medium!!!!) (d/dx)[x!]=??? (3 question marks!!!!! ⇒ hard!!!!!!) Why? Do you?? use so many??? question marks????](https://www.tinkutara.com/question/Q130640.png)
$$\infty^{\infty} =?\:\left(\mathrm{1}\:\mathrm{question}\:\mathrm{mark}!\:\Rightarrow\:\mathrm{easy}!!\right) \\ $$$$\mathrm{0}^{\mathrm{0}} =??\:\left(\mathrm{2}\:\mathrm{question}\:\mathrm{marks}!!!\:\Rightarrow\:\mathrm{medium}!!!!\right) \\ $$$$\frac{{d}}{{dx}}\left[{x}!\right]=???\:\left(\mathrm{3}\:\mathrm{question}\:\mathrm{marks}!!!!!\:\Rightarrow\:\mathrm{hard}!!!!!!\right) \\ $$$$\mathrm{Why}?\:\mathrm{Do}\:\mathrm{you}??\:\mathrm{use}\:\mathrm{so}\:\mathrm{many}???\:\mathrm{question} \\ $$$$\mathrm{marks}???? \\ $$
Commented by Study last updated on 27/Jan/21
$${hhhhhhhhhhhh}!\: \\ $$$${why}\:{do}\:{u}\:{use}\:\:\:\:!!!!? \\ $$
Answered by mathmax by abdo last updated on 27/Jan/21
$$\mathrm{lim}_{\mathrm{x}\rightarrow+\infty} \mathrm{x}^{\mathrm{x}} \:=\mathrm{lim}_{\mathrm{x}\rightarrow+\infty} \mathrm{e}^{\mathrm{xlnx}} \:=\mathrm{e}^{+\infty} \:=+\infty \\ $$