Question Number 183485 by Gamil last updated on 26/Dec/22 $$\:\boldsymbol{\mathrm{L}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\:−\mathrm{2}\boldsymbol{\mathrm{tan}}\:\boldsymbol{\mathrm{x}}\:+\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{2}\boldsymbol{\mathrm{sin}}\:\mathrm{3}\boldsymbol{\mathrm{x}}\:−\mathrm{9}\boldsymbol{\mathrm{x}}^{\mathrm{3}} } \\ $$$$\:\:\boldsymbol{\mathrm{L}}=\:\frac{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2}\boldsymbol{\mathrm{sin}}\:\boldsymbol{\mathrm{x}}\:−\mathrm{2}\boldsymbol{\mathrm{tan}}\:\boldsymbol{\mathrm{x}}\:+\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\boldsymbol{\mathrm{x}}^{\mathrm{5}} }}{\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{6}\boldsymbol{\mathrm{x}}−\mathrm{2}\boldsymbol{\mathrm{sin}}\:\mathrm{3}\boldsymbol{\mathrm{x}}\:−\mathrm{9}\boldsymbol{\mathrm{x}}^{\mathrm{3}} }{\boldsymbol{\mathrm{x}}^{\mathrm{5}} }}\:=\:\frac{\boldsymbol{\mathrm{L}}_{\mathrm{1}} }{\boldsymbol{\mathrm{L}}_{\mathrm{2}} } \\ $$…
Question Number 117818 by snipers237 last updated on 13/Oct/20 $$\:{let}\:{ABC}\:\:{be}\:{a}\:{triangle}\:{AB}={c}\:\:{AC}={b}\:\:{BC}={a} \\ $$$${Show}\:{that}\:{ABC}\:{is}\:{right}\:\Leftrightarrow\:\:{tan}\left(\frac{{B}}{\mathrm{2}}\right)=\frac{{a}+{c}}{{b}}\: \\ $$ Commented by 1549442205PVT last updated on 14/Oct/20 $$\mathrm{Question}\:\mathrm{is}'\mathrm{nt}\:\mathrm{exact}.\mathrm{Example},\Delta\mathrm{ABC} \\ $$$$\mathrm{A}=\mathrm{90}° \\…
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Question Number 183263 by Engr_Jidda last updated on 24/Dec/22 $${Derive}\:{the}\:{formular}\:{that}\:{can}\:{be}\:{used}\: \\ $$$${to}\:{count}\:{the}\:{number}\:{of}\:{dissimilar}\:{surds} \\ $$$${obtaining}\:{after}\:{full}\:{expansion}\:{of} \\ $$$$\left(\sum_{{x}=\mathrm{1}} ^{{n}} \sqrt{{x}}\right)^{\mathrm{4}} \:{where}\:{every}\:{x}\:{term}\:{is}\:{a}\:{prime}\:{number}. \\ $$ Commented by mr W…
Question Number 183236 by a.lgnaoui last updated on 23/Dec/22 $${dererminer}\:\:{la}\:{valeur}\:{x}? \\ $$ Commented by a.lgnaoui last updated on 23/Dec/22 Commented by mr W last updated…
Question Number 117641 by bemath last updated on 13/Oct/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\sqrt{\mathrm{6}−\mathrm{x}}\:>\:\mathrm{x}−\mathrm{4} \\ $$ Answered by Don08q last updated on 13/Oct/20 $$\left(\mathrm{6}−{x}\right)\:>\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} \:{or}\:\left(\mathrm{6}−{x}\right)\:<\:\left({x}−\mathrm{4}\right)^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:{when}\:\:\mathrm{6}\:−\:{x}\:>\:{x}^{\mathrm{2}} −\mathrm{8}{x}+\mathrm{16} \\…
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Question Number 51649 by byaw last updated on 29/Dec/18 $$\mathrm{It}\:\mathrm{takes}\:\mathrm{man}\:\mathrm{A}\:\mathrm{6}\:\mathrm{days}\:\mathrm{to}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of} \\ $$$$\mathrm{work}.\:\mathrm{It}\:\mathrm{takes}\:\mathrm{man}\:\mathrm{B}\:\mathrm{4}\:\mathrm{days}\:\mathrm{to}\:\mathrm{do}\: \\ $$$$\mathrm{the}\:\mathrm{same}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}.\:\mathrm{How}\:\mathrm{many} \\ $$$$\mathrm{days}\:\mathrm{will}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{take}\:\mathrm{to}\:\mathrm{do}\:\mathrm{the} \\ $$$$\mathrm{same}\:\mathrm{piece}\:\mathrm{of}\:\mathrm{work}? \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated…
Question Number 117116 by mathocean1 last updated on 10/Oct/20 $${x}\:,\:{y}\:,{z}\:,\:{t}\:\in\:\mathbb{Z}. \\ $$$${x}\:{and}\:{y}\:{are}\:{x}\:{are}\:{respectively}\:{the} \\ $$$${divisor}\:{of}\:{y}\:{and}\:{t}. \\ $$$${Justify}\:{the}\:{existence}\:{of}\:{k}\:\in\:\mathbb{Z}\:{such} \\ $$$${that}\:{yt}={xzk}. \\ $$$${Deduct}\:{that}\:{x}^{{m}\:} {is}\:{a}\:{divisor}\:{of}\:{y}^{{m}} \\ $$$${where}\:{m}\:\in\:\mathbb{N}. \\ $$…
Question Number 117007 by TANMAY PANACEA last updated on 08/Oct/20 $${find}\:{unit}\:{digit}\:{of} \\ $$$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!+\mathrm{5}!+….+\mathrm{100}! \\ $$ Answered by mindispower last updated on 08/Oct/20 $${if}\:{n}\geqslant\mathrm{5}\:{n}!=\mathrm{0}\left(\mathrm{10}\right) \\ $$$$\mathrm{1}+\mathrm{2}!+\mathrm{3}!+\mathrm{4}!=\mathrm{24}+\mathrm{6}+\mathrm{4}+\mathrm{1}=\mathrm{35}…