Question Number 915 by 112358 last updated on 24/Apr/15 $${Show}\:{that}\:\forall{t}\geqslant\mathrm{0}\:,\:{x}\leqslant\mathrm{1}\:{where} \\ $$$${x}=\frac{{e}^{−{t}} }{\mathrm{2}}\left({t}^{\mathrm{2}} +\mathrm{2}{t}+\mathrm{2}\right)\:\:,\:{t}\in\mathbb{R}.\: \\ $$ Commented by 123456 last updated on 24/Apr/15 $${t}\geqslant\mathrm{0}\Leftrightarrow−{t}\leqslant\mathrm{0}\Leftrightarrow{e}^{−{t}} \leqslant{e}^{\mathrm{0}}…
Question Number 908 by 112358 last updated on 20/Apr/15 $${Show}\:{that}\:{for}\:{the}\:{system}\:{of}\: \\ $$$${equations} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}+{y}+{z}=\mathrm{3} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}{x}+\mathrm{2}{y}+\mathrm{2}{z}=\mathrm{6} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}{x}+\mathrm{3}{y}+\mathrm{3}{z}=\mathrm{9} \\ $$$${the}\:{general}\:{solution}\:{is}\:{given}\:{by} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}=\lambda+\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{y}=\mu+\mathrm{1} \\…
Question Number 66431 by hmamarques1994@gmail.com last updated on 15/Aug/19 $$\: \\ $$$$\:\boldsymbol{\mathrm{Determine}}\:\:\boldsymbol{\mathrm{x}}\:\:\boldsymbol{\mathrm{e}}\:\:\boldsymbol{\mathrm{y}}: \\ $$$$\: \\ $$$$\:\begin{cases}{\boldsymbol{\mathrm{x}}^{\frac{\mathrm{1}}{\:\sqrt{\boldsymbol{\mathrm{i}}}}} +\:\frac{\mathrm{1}}{\boldsymbol{\mathrm{y}}^{\boldsymbol{\mathrm{i}}\sqrt{\boldsymbol{\mathrm{i}}}} }\:=\:\mathrm{10}}\\{\frac{\mathrm{1}}{\left(\boldsymbol{\mathrm{xy}}\right)^{\boldsymbol{\mathrm{i}}\sqrt{\boldsymbol{\mathrm{i}}}} }\:=\:\mathrm{21}}\end{cases} \\ $$$$\: \\ $$ Answered by…
Question Number 891 by 123456 last updated on 17/Apr/15 $$\mathrm{lets}\:{f}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{lets}\:{e}_{{n}} :\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{lets}\:{a}_{{n}} :\left[\mathrm{0},\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\mathrm{such}\:\mathrm{that} \\ $$$${f}\left({x}\right)=\underset{{i}=\mathrm{1}} {\overset{\mathrm{3}} {\sum}}{a}_{{i}} \left({x}\right){e}_{{i}} \left({x}\right) \\…
Question Number 131953 by SLVR last updated on 10/Feb/21 $$ \\ $$ Commented by SLVR last updated on 10/Feb/21 Terms of Service Privacy Policy Contact:…
Question Number 66412 by aliesam last updated on 14/Aug/19 $${if} \\ $$$$ \\ $$$${f}\left({x}\right)={ln}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right) \\ $$$$ \\ $$$${find} \\ $$$$ \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\…
Question Number 131924 by aurpeyz last updated on 09/Feb/21 $${is}\:{there}\:{any}\:{diffrence}\:{btw}\:\mathrm{060}\:{and}\:\mathrm{60}^{\mathrm{0}} \\ $$ Answered by physicstutes last updated on 10/Feb/21 $$\mathrm{I}\:\mathrm{think}:\:\mathrm{one}\:\mathrm{just}\:\mathrm{specifies}\:\mathrm{that}\:\mathrm{you}'\mathrm{ve}\:\mathrm{taken}\:\mathrm{it}\:\mathrm{clockwise} \\ $$$$\mathrm{from}\:\mathrm{0}°\:\mathrm{to}\:\mathrm{60}°\:\mathrm{while}\:\mathrm{the}\:\mathrm{other}\:\mathrm{doesn}'\mathrm{t} \\ $$$$\mathrm{60}°\:\mathrm{could}\:\mathrm{mean}\:\mathrm{clockwise}\:\mathrm{or}\:\mathrm{counter}\:\mathrm{clockwise}\:\mathrm{but}\:\mathrm{if}\:\mathrm{you}\:\mathrm{mean} \\…
Question Number 855 by 112358 last updated on 26/Mar/15 $${Find}\:{the}\:{number}\:{of}\:{terms}\:{in} \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{101}} \left(\mathrm{1}+{x}^{\mathrm{2}} −{x}\right)^{\mathrm{100}} . \\ $$ Answered by prakash jain last updated on 26/Mar/15…
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Question Number 66379 by Sandy Suhendra last updated on 13/Aug/19 Commented by kaivan.ahmadi last updated on 13/Aug/19 $$={lim}_{{x}\rightarrow\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{3}{cosx}+\mathrm{5}{cos}\mathrm{3}{x}}{{cot}\mathrm{5}{x}}\:\overset{{hop}} {=} \\ $$$${lim}_{{x}\rightarrow\frac{.\pi}{\mathrm{2}}} \:\:\frac{−\mathrm{3}{sinx}−\mathrm{15}{sin}\mathrm{3}{x}}{−\mathrm{5}\left(\mathrm{1}+{cot}^{\mathrm{2}} \mathrm{5}{x}\right)}=\frac{−\mathrm{3}+\mathrm{15}}{−\mathrm{5}}=−\frac{\mathrm{12}}{\mathrm{5}} \\…