Question Number 2649 by Filup last updated on 24/Nov/15 $$\mathrm{Ok}\:\mathrm{guys}.\:\mathrm{We}\:\mathrm{all}\:\mathscr{LOVE}\:\mathrm{mathematics}. \\ $$$$\mathrm{So},\:\mathrm{I}\:\mathrm{have}\:\mathrm{came}\:\mathrm{up}\:\mathrm{with}\:\mathrm{a}\:\mathrm{simple}\:\mathrm{and} \\ $$$$\mathrm{possibly}\:\mathrm{effect}\:\mathrm{way}\:\mathrm{to}\:\mathrm{not}\:\mathrm{only}\:\mathrm{improve} \\ $$$$\mathrm{our}\:\mathrm{abilities}\:\mathrm{as}\:\mathrm{mathematicians},\:\mathrm{but}\:\mathrm{also} \\ $$$$\mathrm{have}\:\mathrm{some}\:\mathrm{fun},\:\mathrm{too}. \\ $$$$ \\ $$$$\mathrm{We}\:\mathrm{should}\:\mathrm{hold}\:\mathrm{a}\:\mathrm{competition}\:\mathrm{every} \\ $$$$\mathrm{now}\:\mathrm{and}\:\mathrm{again}.\:\mathrm{We}\:\mathrm{can},\:\mathrm{for}\:\mathrm{example} \\…
Question Number 133722 by I want to learn more last updated on 23/Feb/21 Answered by mr W last updated on 23/Feb/21 $${x}=\mathrm{28}\left(\mathrm{tan}\:\mathrm{40}−\mathrm{tan}\:\mathrm{20}\right) \\ $$ Answered…
Question Number 68183 by ajfour last updated on 06/Sep/19 Commented by ajfour last updated on 06/Sep/19 $${QBC}\:{and}\:{BPD}\:{are}\:{tangent}\:{and} \\ $$$${normal}\:{respectively}\:{to} \\ $$$${the}\:{cubic}\:{function}\:{y}={x}^{\mathrm{3}} −\mathrm{19}{x}+\mathrm{30} \\ $$$${at}\:{one}\:{of}\:{its}\:{root}\:{and}\:{QAD}\:{and} \\…
Question Number 133719 by leena12345 last updated on 23/Feb/21 Commented by leena12345 last updated on 23/Feb/21 $${help} \\ $$ Answered by bramlexs22 last updated on…
Question Number 2645 by Filup last updated on 24/Nov/15 $${A}=\int_{{N}_{\mathrm{1}} } ^{{N}_{\mathrm{2}} } \lfloor{x}\rfloor{dx} \\ $$$$\left({N}_{\mathrm{1}} ,\:{N}_{\mathrm{2}} \right)\in\mathbb{Z},\:\:\:{N}_{\mathrm{1}} <{N}_{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:{A} \\ $$…
Question Number 2644 by 123456 last updated on 24/Nov/15 $${a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} }{{n}}+{n} \\ $$$${a}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{{n}} =???\:{n}\in\mathbb{N}^{\ast} \\ $$ Commented by RasheedAhmad last updated…
Question Number 68178 by Mikael last updated on 06/Sep/19 $$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:\frac{\left({cosx}\right)^{{sin}\mathrm{2}{x}} −\mathrm{1}}{{x}^{\mathrm{3}} }=? \\ $$ Commented by mathmax by abdo last updated on 06/Sep/19 $${let}\:{f}\left({x}\right)\:=\frac{\left({cosx}\right)^{{sin}\left(\mathrm{2}{x}\right)}…
Question Number 2642 by Rasheed Soomro last updated on 24/Nov/15 $${n}\:{lines}\:{are}\:{drawn}\:{inside}\:{a}\:{circle}\:{in}\:{such}\:{a}\:{way}\:{that}\: \\ $$$${the}\:{circle}\:{has}\:{been}\:{divided}\:{in}\:{maximum}\:{number}\:{of} \\ $$$${parts}.\:{Determine}\:{this}\:{maximum}\:{number}. \\ $$ Commented by RasheedAhmad last updated on 24/Nov/15 $$\bullet{One}\:{line}\:{can}\:{divide}\:{the}\:{circle}…
Question Number 133708 by Dwaipayan Shikari last updated on 23/Feb/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{cos}\left(\left(\pi+{e}\right){n}\right)}{{n}^{\mathrm{4}} } \\ $$ Answered by mindispower last updated on 24/Feb/21 $$\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{{sin}\left({nx}\right)}{{n}}={Im}\:\underset{{n}\geqslant\mathrm{1}}…
Question Number 68171 by naka3546 last updated on 06/Sep/19 Commented by mathmax by abdo last updated on 06/Sep/19 $$ \\ $$$$\sqrt{\mathrm{5}−\mathrm{2}\sqrt{{x}}\:}\:{is}\:{not}\:{defined}\:{on}\:+\infty\:! \\ $$ Commented by…