Question Number 212405 by mathlove last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\mathrm{lim}}\frac{{e}^{{x}} −{e}^{\mathrm{3}} }{{x}−\mathrm{3}}=? \\ $$ Answered by som(math1967) last updated on 13/Oct/24 $$\underset{{x}\rightarrow\mathrm{3}} {\:{lim}}\frac{{e}^{\mathrm{3}} \left({e}^{{x}−\mathrm{3}}…
Question Number 212432 by hardmath last updated on 13/Oct/24 $$\frac{\mathrm{9}}{\mathrm{2}\centerdot\mathrm{4}}\:+\:\frac{\mathrm{9}}{\mathrm{4}\centerdot\mathrm{6}}\:+…+\:\frac{\mathrm{9}}{\mathrm{4n}\centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)}\:=\:\frac{\mathrm{15}}{\mathrm{8}} \\ $$$$\mathrm{Find}:\:\:\boldsymbol{\mathrm{n}}\:=\:? \\ $$ Answered by Ar Brandon last updated on 13/Oct/24 $$\mathrm{9}\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{4}{n}\left({n}+\mathrm{1}\right)}=\frac{\mathrm{15}}{\mathrm{8}}…
Question Number 212435 by Ar Brandon last updated on 13/Oct/24 Answered by mr W last updated on 13/Oct/24 $${y}'=−\frac{\mathrm{2}{y}^{\mathrm{2}} +{xy}}{{x}^{\mathrm{2}} +{xy}+{y}^{\mathrm{2}} } \\ $$$${let}\:{y}={px} \\…
Question Number 212428 by Spillover last updated on 13/Oct/24 Answered by Yassine84 last updated on 13/Oct/24 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}} \right)\:{then} \\ $$$${li}\underset{\mathrm{1}} {{m}}\:\frac{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)\left(\mathrm{1}+{x}^{\mathrm{3}} \right)\left(\mathrm{1}+{x}^{\mathrm{4}}…
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Question Number 212424 by hardmath last updated on 13/Oct/24 $$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:−\:\mathrm{3z}\:=\:\mathrm{1}}\\{\mathrm{2x}\:−\:\mathrm{y}\:+\:\mathrm{z}\:=\:\mathrm{4}}\\{\mathrm{3x}\:+\:\mathrm{y}\:+\:\mathrm{2z}\:=\:\mathrm{7}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{x},\mathrm{y},\mathrm{z}\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $$\left({ii}\right)+\left({iii}\right)\Rightarrow\mathrm{5}{x}+\mathrm{3}{z}=\mathrm{11}…\left({iv}\right) \\ $$$$\mathrm{2}\left({iii}\right)−\left({i}\right)\Rightarrow\mathrm{5}{x}+\mathrm{7}{z}=\mathrm{13}…\left({v}\right) \\ $$$$\left({v}\right)−\left({iv}\right)\Rightarrow\mathrm{4}{z}=\mathrm{2}\Rightarrow{z}=\frac{\mathrm{1}}{\mathrm{2}}\Rightarrow{x}=\frac{\mathrm{19}}{\mathrm{10}}\Rightarrow{y}=\frac{\mathrm{3}}{\mathrm{10}} \\…
Question Number 212427 by Spillover last updated on 13/Oct/24 Commented by Ghisom last updated on 13/Oct/24 $$−\frac{\mathrm{1}}{\mathrm{10}×\mathrm{10}!} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 212448 by hardmath last updated on 13/Oct/24 $$\mathrm{If}\:\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{x}\:+\:\mathrm{3}\:=\:\mathrm{0} \\ $$$$\mathrm{Find}\:\:\mathrm{x}\:+\:\frac{\mathrm{9}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by A5T last updated on 13/Oct/24 $${x}^{\mathrm{2}} −{x}+\mathrm{3}=\mathrm{0}\Rightarrow{x}^{\mathrm{3}}…
Question Number 212416 by MrGaster last updated on 13/Oct/24 $$\frac{\frac{\int_{\mathrm{0}} ^{+\infty} {e}^{−{s}} {s}^{\mathrm{5}} {ds}}{\mathrm{2}}+\frac{\int_{−\infty} ^{+\infty} {e}^{−\frac{{t}^{\mathrm{2}} }{\mathrm{2}}} {dt}}{\int_{\mathrm{0}} ^{+\infty} \mathrm{sin}{t}^{\mathrm{2}} {dt}}\left(\frac{\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}{n}+\mathrm{1}}}{\int_{\mathrm{0}} ^{+\infty}…
Question Number 212417 by mr W last updated on 13/Oct/24 Commented by mr W last updated on 13/Oct/24 $${unsolved}\:{old}\:{question}\:\mathrm{212291} \\ $$ Answered by mr W…