Category: Limits

Question Number 20138 by tammi last updated on 22/Aug/17 $$\underset{x\to 0}{\lim }\frac{1-\cos ax}{1-\cos bx}$$$$$$ Answered by ajfour last updated on 22/Aug/17 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2sin}\:^{\mathrm{2}} \left(\frac{{ax}}{\mathrm{2}}\right)}{\mathrm{2sin}\:^{\mathrm{2}}…

Question Number 151111 by alcohol last updated on 18/Aug/21 Answered by Olaf_Thorendsen last updated on 18/Aug/21 $$\mathrm{On}\mathrm{peut}\mathrm{eventuellement}\mathrm{avoir}3\mathrm{balles}$$$$\mathrm{noires}\mathrm{au}\mathrm{cours}\mathrm{des}3,4,5,\dots k\mathrm{premiers}$$$$\mathrm{tirages}\mathrm{mais}\mathrm{pour}\mathrm{en}\mathrm{etre}\mathrm{certain},\mathrm{il}\mathrm{faut}$$$$\mathrm{au}\mathrm{moins}\mathrm{tirer}1003\mathrm{balles}.$$$$\mathrm{Au}\:\mathrm{pire},\:\mathrm{on}\:\mathrm{aurait}\:\mathrm{500}\:\mathrm{balles}\:\mathrm{blanches},…

Question Number 151001 by EDWIN88 last updated on 17/Aug/21 $$$$$$\underset{x\to 0}{\lim }\frac{\sqrt[3]{2+\sin {}^{2}x}-\sqrt[3]{1+\cos 2x}}{x\tan x}=?$$$$$$ Answered by john_santu last updated on 17/Aug/21…

Question Number 85293 by jagoll last updated on 20/Mar/20 $$\underset{x\to 0^{+}}{\lim }\sqrt{\frac{1}{\mathrm{x}}}-\sqrt{\frac{1}{2\mathrm{x}}-2020}?$$ Commented by jagoll last updated on 20/Mar/20 $$\mathrm{what}\mathrm{is}\mathrm{result}?0\mathrm{or}\mathrm{\infty }?$$ Answered…

Question Number 150654 by mnjuly1970 last updated on 14/Aug/21 Answered by Ar Brandon last updated on 14/Aug/21 $${S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \left(\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{1}}−\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{2}}\right) \…