Question Number 145444 by mathdanisur last updated on 04/Jul/21 $$\frac{\mathrm{1}}{\mathrm{2}}\:-\:\frac{\mathrm{3}}{\mathrm{4}}\:+\:\frac{\mathrm{7}}{\mathrm{8}}\:-\:\frac{\mathrm{15}}{\mathrm{16}}\:+\:…\:=\:? \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21 $$\mathrm{S}\:=\:\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}} \frac{\mathrm{2}^{{n}+\mathrm{1}} −\mathrm{1}}{\mathrm{2}^{{n}+\mathrm{1}} }…
Question Number 145442 by ArielVyny last updated on 04/Jul/21 $${soit}\:{z}\in\mathbb{C}\:{montrer}\:{que}\:{cos}\left({z}\right)\:{et}\:{sin}\:\left({z}\right) \\ $$$${ne}\:{sont}\:{pas}\:{bornees} \\ $$$${que}\:{vaut}\:{sin}^{\mathrm{2}} \left({z}\right)+{cos}^{\mathrm{2}} \left({z}\right)=?? \\ $$ Answered by Olaf_Thorendsen last updated on 05/Jul/21…
Question Number 145436 by mathdanisur last updated on 04/Jul/21 Commented by justtry last updated on 05/Jul/21 Commented by mathdanisur last updated on 05/Jul/21 $${thanks}\:{Ser},\:{but}\:{wrong} \\…
Question Number 14354 by tawa tawa last updated on 30/May/17 Answered by mrW1 last updated on 31/May/17 $$\mathrm{2}. \\ $$$${mean}=\left(\mathrm{60}+\mathrm{62}+\mathrm{65}+\mathrm{68}+\mathrm{79}\right)/\mathrm{5}=\mathrm{66}.\mathrm{8} \\ $$$${the}\:{number}\:{close}\:{to}\:{mean}\:{is}\:\mathrm{68}\:{kg}. \\ $$$$\Rightarrow{D} \\…
Question Number 79883 by MJS last updated on 29/Jan/20 $$\mathrm{to}\:\mathrm{Sir}\:\mathrm{Jagoll}\:\left({and}\:{of}\:{course}\:{everybody}\:{else}\right) \\ $$$$ \\ $$$$\left(\mathrm{1}\right) \\ $$$${y}=\frac{{x}^{\mathrm{2}} −{x}−\mathrm{6}}{{x}^{\mathrm{2}} −\mathrm{3}{x}−\mathrm{4}}= \\ $$$$=\frac{\left({x}−\mathrm{3}\right)\left({x}+\mathrm{2}\right)}{\left({x}−\mathrm{4}\right)\left({x}+\mathrm{1}\right)}\:\Rightarrow \\ $$$$\Rightarrow\:\begin{cases}{\mathrm{zeros}\:\mathrm{at}\:{x}=−\mathrm{2};\:{x}=\mathrm{3}}\\{\mathrm{vertical}\:\mathrm{asymptotes}\:\mathrm{at}\:{x}=−\mathrm{1};\:{x}=\mathrm{4}}\end{cases} \\ $$$$\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{R}\backslash\left\{−\mathrm{1};\:\mathrm{4}\right\} \\…
Question Number 79876 by mathocean1 last updated on 28/Jan/20 $${f}\:{is}\:{derivable}\:{in}\:\mathbb{R}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Demonstrate}\:\mathrm{that}\:\mathrm{if}\:{f}\:\mathrm{is}\:\mathrm{pair}\:,\:{f}\:'\:\mathrm{is}\:\mathrm{odd}\left(\mathrm{unpair}\right). \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Demonstrate}\:\mathrm{that}\:\mathrm{if}\:{f}\:{is}\:\mathrm{unpair}\:,\:{f}\:'\:\mathrm{is}\:\mathrm{pair}. \\ $$$$ \\ $$$$\mathrm{Please}\:\mathrm{help}\:\mathrm{me}\:\mathrm{sirs} \\ $$ Commented by MJS last updated…
Question Number 145411 by puissant last updated on 04/Jul/21 $$\mathrm{un}\:\mathrm{espace}\:\mathrm{vectoriel}\:\mathrm{n}'\mathrm{as}\:\mathrm{un}\:\mathrm{seul}\: \\ $$$$\mathrm{hyper}-\mathrm{plan}..\:\mathrm{quelle}\:\mathrm{est}\:\mathrm{sa}\:\mathrm{dimension}.? \\ $$ Answered by Olaf_Thorendsen last updated on 04/Jul/21 $$\mathrm{L}'\mathrm{une}\:\mathrm{des}\:\mathrm{definitions}\:\mathrm{des}\:\mathrm{hyperplans} \\ $$$$\mathrm{entraine}\:\mathrm{dim}\left(\mathrm{H}\right)\:=\:\mathrm{dim}\left(\mathrm{E}\right)−\mathrm{1}\:=\:{n}−\mathrm{1} \\…
Question Number 145406 by mathdanisur last updated on 04/Jul/21 $${if}\:\:\boldsymbol{{log}}_{\boldsymbol{{a}}} \boldsymbol{{c}}+\boldsymbol{{log}}_{\boldsymbol{{c}}} \boldsymbol{{b}}=\mathrm{2}\:;\:\boldsymbol{{log}}_{\boldsymbol{{b}}} \boldsymbol{{c}}+\boldsymbol{{log}}_{\boldsymbol{{a}}} \boldsymbol{{c}}=\mathrm{0} \\ $$$${find}\:\:\frac{\mathrm{1}}{\boldsymbol{{log}}_{\boldsymbol{{a}}} \boldsymbol{{b}}}\:+\:\frac{\mathrm{1}}{\boldsymbol{{log}}_{\boldsymbol{{b}}} \boldsymbol{{c}}}\:+\:\frac{\mathrm{1}}{\boldsymbol{{log}}_{\boldsymbol{{c}}} \boldsymbol{{a}}}\:=\:? \\ $$ Answered by som(math1967) last…
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Question Number 79861 by M±th+et£s last updated on 28/Jan/20 Commented by mr W last updated on 29/Jan/20 $${proof}\:{see}\:{Q}\mathrm{79932}! \\ $$ Terms of Service Privacy Policy…