Question Number 203061 by York12 last updated on 08/Jan/24 $$\mathrm{14}\int\frac{\mathrm{1}}{\mathrm{x}\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} \:}\:\:\mathrm{d}\left(\mathrm{x}\right) \\ $$ Answered by MM42 last updated on 09/Jan/24 $${ans} \\ $$$$\:\frac{−\mathrm{7}}{\left({lnx}\right)^{\mathrm{2}} } \\…
Question Number 203059 by hassanmpsy last updated on 08/Jan/24 Commented by witcher3 last updated on 11/Jan/24 $$\mathrm{U}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{n}\left(\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}\right)}{\mathrm{n}^{\mathrm{2}} \left(\mathrm{2}+\mathrm{2}\frac{\mathrm{k}}{\mathrm{n}}+\left(\frac{\mathrm{k}}{\mathrm{n}}\right)^{\mathrm{2}} \right)}=\frac{\mathrm{1}}{\mathrm{n}}\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{f}\left(\frac{\mathrm{k}}{\mathrm{n}}\right) \\…
Question Number 203055 by mr W last updated on 08/Jan/24 Commented by mr W last updated on 08/Jan/24 $${is}\:{it}\:{possible}\:{to}\:{determine}\:{the}\: \\ $$$${unknown}\:{area}\:{in}\:{terms}\:{of}\:{other} \\ $$$${partial}\:{areas}\:{A},{B},{C},{D},{E}? \\ $$…
Question Number 203051 by ajfour last updated on 08/Jan/24 $${A}\:{two}\:{digit}\:{number}\:\:\left({AB}\right)_{\mathrm{10}} \\ $$$$\left({AB}\right)_{\mathrm{10}} −{A}^{{B}} =\left({BA}\right)_{\mathrm{10}} \\ $$$${Find}\:{the}\:{number}.\:{There}\:{is}\:{a}\:{poem}. \\ $$$${Having}\:{arrived}\:{at}\:{the}\:{age}\:{of}\:\left({BA}\right)_{\mathrm{10}} . \\ $$ Answered by Rasheed.Sindhi last…
Question Number 203045 by MathematicalUser2357 last updated on 08/Jan/24 $${very}\:{old}\:{q}\:{Q}.\mathrm{2} \\ $$ Commented by lazyboy last updated on 11/Jan/24 $${how}\:{can}\:{find}\:{Q}.\mathrm{2} \\ $$ Terms of Service…
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Question Number 203000 by sonukgindia last updated on 07/Jan/24 Answered by SEKRET last updated on 07/Jan/24 $$\mathrm{3};\mathrm{6} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 203002 by mr W last updated on 07/Jan/24 $${Solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{x}−\mathrm{3}=\mathrm{0} \\ $$ Answered by ajfour last updated on 07/Jan/24 $${p}^{\mathrm{2}} \left({p}^{\mathrm{4}}…
Question Number 203035 by Frix last updated on 07/Jan/24 $$\mathrm{e}=\mathrm{2} \\ $$$$\mathrm{Proof}: \\ $$$$\mathrm{Let}\:{x}=\frac{\mathrm{e}+\mathrm{2}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}=\mathrm{e}+\mathrm{2} \\ $$$$\mathrm{2}{x}\left(\mathrm{e}−\mathrm{2}\right)=\left(\mathrm{e}+\mathrm{2}\right)\left(\mathrm{e}−\mathrm{2}\right) \\ $$$$\mathrm{2e}{x}−\mathrm{4}{x}=\mathrm{e}^{\mathrm{2}} −\mathrm{4} \\ $$$$−\mathrm{4}{x}+\mathrm{4}=−\mathrm{2e}{x}+\mathrm{e}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}}…
Question Number 203031 by sonukgindia last updated on 07/Jan/24 Answered by MathematicalUser2357 last updated on 08/Jan/24 $${find}\:\mathrm{8}\:{roots}\:{using}\:{newton}'{s}\:{method} \\ $$ Commented by Calculusboy last updated on…