Menu Close

Category: None

Question-120131

Question Number 120131 by huotpat last updated on 29/Oct/20 Commented by Dwaipayan Shikari last updated on 29/Oct/20 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{\mathrm{2}^{{x}} −\mathrm{2}^{\mathrm{3}} }{{sin}\left(\pi{x}\right)}=\mathrm{2}^{\mathrm{3}} \frac{\mathrm{2}^{{x}−\mathrm{3}} −\mathrm{1}}{{sin}\left(\mathrm{3}\pi−\pi{x}\right)} \\ $$$$=\mathrm{2}^{\mathrm{3}}…

Question-120127

Question Number 120127 by huotpat last updated on 29/Oct/20 Answered by Dwaipayan Shikari last updated on 29/Oct/20 $$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\mathrm{1}−{x}+{logx}}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$$$=\frac{\mathrm{1}−{x}+{log}\left(\mathrm{1}+{x}−\mathrm{1}\right)}{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{\mathrm{1}−{x}+{x}−\mathrm{1}−\frac{\left({x}−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{2}}+\frac{\left({x}−\mathrm{1}\right)^{\mathrm{3}} }{\mathrm{3}}−…}{\left({x}−\mathrm{1}\right)^{\mathrm{2}}…

What-is-d-dx-u-x-v-x-w-x-and-more-generally-what-is-d-dx-i-1-n-u-i-x-Thank-you-

Question Number 54588 by hassentimol last updated on 07/Feb/19 $$\mathrm{What}\:\mathrm{is}\:: \\ $$$$\:\:\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:{u}\left({x}\right)\:×\:{v}\left({x}\right)\:×\:{w}\left({x}\right)\:\right]\:=\:… \\ $$$$ \\ $$$$\mathrm{and}\:\mathrm{more}\:\mathrm{generally},\:\mathrm{what}\:\mathrm{is}\:: \\ $$$$\:\:\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\prod}}\:{u}_{{i}} \left({x}\right)\right]\:=\:… \\ $$$$ \\ $$$$\mathrm{Thank}\:\mathrm{you}…

De-terminer-a-b-et-c-trois-termes-conse-quences-d-une-suite-ge-ometrique-tels-que-a-b-c-36-75-abc-343-

Question Number 185625 by LEKOUMA last updated on 24/Jan/23 $${D}\acute {{e}terminer}\:{a},\:{b}\:{et}\:{c}\:{trois}\:{termes}\:{cons}\acute {{e}quences} \\ $$$${d}'{une}\:{suite}\:{g}\acute {{e}ometrique}\:{tels}\:{que}: \\ $$$$\begin{cases}{{a}+{b}+{c}=\mathrm{36},\mathrm{75}}\\{{abc}=\mathrm{343}}\end{cases} \\ $$ Answered by mr W last updated…