Question Number 197272 by Erico last updated on 12/Sep/23 $$\mathrm{How}\:\mathrm{to}\:\mathrm{calculate}\:\mathrm{this}\:\mathrm{integral} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \:\frac{\mathrm{ln}\left(\mathrm{1}+{sint}\right)}{{sint}}{dt} \\ $$ Answered by Mathspace last updated on 12/Sep/23 $${tan}\left(\frac{{t}}{\mathrm{2}}\right)={x}\:\Rightarrow \\…
Question Number 197274 by sonukgindia last updated on 12/Sep/23 Commented by TheHoneyCat last updated on 18/Sep/23 Can you please provide the definitions on these factorials? (I only know "n!") Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197275 by uchihayahia last updated on 08/Oct/23 $$ \\ $$$$\:{how}\:{do}\:{i}\:{prove}\:{this},\:{help}\:{please}. \\ $$$$\:\mid\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\mid\leqslant\frac{\mathrm{5}}{\mathrm{4}},\mid{x}\mid\leqslant\mathrm{2} \\ $$$$ \\ $$$$ \\ $$ Answered by AST…
Question Number 197297 by hardmath last updated on 12/Sep/23 $$\mathrm{677} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 197299 by bbbbbbbb last updated on 12/Sep/23 $$\sqrt[{\mathrm{6}}]{−\mathrm{64}}−\sqrt[{\mathrm{10}}]{−\mathrm{10}}=? \\ $$$$\boldsymbol{{I}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{so}}\:\boldsymbol{\mathrm{much}}\:\boldsymbol{\mathrm{plz}} \\ $$ Answered by Frix last updated on 13/Sep/23 $$\forall{n}\in\mathbb{N}\backslash\left\{\mathrm{0}\right\}:\:−{n}={n}\mathrm{e}^{\mathrm{i}\pi} \:\Rightarrow \\ $$$$\sqrt[{{k}}]{−{n}}=\sqrt[{{k}}]{{n}}\mathrm{e}^{\mathrm{i}\frac{\pi}{{k}}}…
Question Number 197292 by universe last updated on 12/Sep/23 $$\:\:\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\int_{\mathrm{0}\:} ^{\mathrm{1}} \frac{{nx}^{{n}−\mathrm{1}} }{\mathrm{1}+{x}}{dx}\:\:=\:\:\:? \\ $$ Answered by witcher3 last updated on 12/Sep/23 $$\mathrm{2x}\leqslant\mathrm{1}+\mathrm{x}\leqslant\mathrm{2},\forall\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\…
Question Number 197290 by sonukgindia last updated on 12/Sep/23 Commented by mahdipoor last updated on 12/Sep/23 $${log}_{\mathrm{7}} {A}={log}_{\mathrm{7}} \left(\frac{\mathrm{36}}{\mathrm{9}}\right)\Rightarrow{A}=\mathrm{4}\Rightarrow{log}_{\mathrm{2}} {A}=\mathrm{2} \\ $$ Terms of Service…
Question Number 197287 by MM42 last updated on 13/Sep/23 $${answer}\:{to}\:{the}\:{question}\:{number} \\ $$$$\mathrm{197017} \\ $$$${AF}={FI}\:\&\:\:{AG}={GJ}\Rightarrow{FG}=\frac{\mathrm{1}}{\mathrm{2}}{IJ}=\frac{\mathrm{1}}{\mathrm{6}}{BC} \\ $$$$\bigtriangleup{FGH}\:\:{is}\:\:{squilatral}\:\Rightarrow\:\bigtriangleup{FGH}\approx\bigtriangleup{ABC} \\ $$$$\Rightarrow\frac{{S}_{{FGH}} }{{S}_{{SBC}} }\:=\frac{\mathrm{1}}{\mathrm{36}\:}\:\checkmark \\ $$$$ \\ $$ Commented…
Question Number 197281 by cortano12 last updated on 12/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{x}+\mathrm{2x}^{\mathrm{5}} }{\mathrm{3x}^{\mathrm{3}} }\:=? \\ $$ Answered by MM42 last updated on 12/Sep/23 $${lim}_{{x}\rightarrow\mathrm{0}} \:\frac{−\frac{\mathrm{1}}{\mathrm{6}}{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{5}}…
Question Number 197282 by cortano12 last updated on 12/Sep/23 $$\:\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}−\mathrm{sin}\:\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} \:\left(\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}−\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} \:\right)}\:=? \\ $$ Answered by MM42 last updated on 12/Sep/23…