Question Number 210967 by mahdipoor last updated on 24/Aug/24 $${Q}.\mathrm{210956} \\ $$$${im}\:{read}\:{leithold}\:{book}\:{again}\:,\:{in}\:{this}\:{book}\:: \\ $$$$\left.\mathrm{1}\right\}{define}\::\:{ln}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {dx}/{x}\:\:\:\:\:\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right\}{define}\::\:{ln}\left({e}\right)=\mathrm{1}=\int_{\mathrm{1}} ^{\:{e}} {dx}/{x} \\ $$$$\left.\mathrm{3}\right\}{define}\::\:{exp}\left({x}\right)={y}\:\Leftrightarrow\:{ln}\left({y}\right)={x} \\ $$$$\frac{{d}\left({ln}\left({u}\right)\right)}{{du}}=\frac{\mathrm{1}}{{u}}\:\Rightarrow\:\frac{{d}\left({ln}\left({u}\right)\right)}{{dx}}=\frac{{du}/{dx}}{{u}}\:\Rightarrow \\…
Question Number 210961 by RojaTaniya last updated on 24/Aug/24 Answered by A5T last updated on 24/Aug/24 $$\frac{{a}−\mathrm{1}+\mathrm{2}}{{a}−\mathrm{1}}+\frac{{b}−\mathrm{1}+\mathrm{2}}{{b}−\mathrm{1}}+\frac{{c}−\mathrm{1}+\mathrm{2}}{{c}−\mathrm{1}}=\mathrm{10} \\ $$$$\Rightarrow\frac{\mathrm{1}}{{a}−\mathrm{1}}+\frac{\mathrm{1}}{{b}−\mathrm{1}}+\frac{\mathrm{1}}{{c}−\mathrm{1}}=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$${a}+{b}+{c}=\mathrm{0};{ab}+{bc}+{ca}=\frac{{m}−\mathrm{1}}{{m}};{abc}=\frac{−{m}−\mathrm{1}}{{m}} \\ $$$$\Rightarrow\frac{{ab}+{bc}+{ca}−\mathrm{2}\left({a}+{b}+{c}\right)+\mathrm{3}}{{abc}−{ab}−{bc}−{ac}+{a}+{b}+{c}−\mathrm{1}}=\frac{\mathrm{7}}{\mathrm{2}} \\ $$$$\Rightarrow\frac{\frac{{m}−\mathrm{1}+\mathrm{3}{m}}{{m}}}{\frac{−{m}−\mathrm{1}+\mathrm{1}−{m}−{m}}{{m}}}=\frac{\mathrm{7}}{\mathrm{2}}\Rightarrow\frac{\mathrm{4}{m}−\mathrm{1}}{−\mathrm{3}{m}}=\frac{\mathrm{7}}{\mathrm{2}}…
Question Number 210956 by mahdipoor last updated on 23/Aug/24 $${we}\:{define}\::\:{ln}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} \frac{{dx}}{{x}} \\ $$$${how}\:{prove}\::\:{ln}\left({x}\right)={log}_{{e}} {x}\:\:\:? \\ $$ Commented by Ghisom last updated on 24/Aug/24 $$\mathrm{an}\:\mathrm{idea}:…
Question Number 210948 by cherokeesay last updated on 23/Aug/24 Commented by cherokeesay last updated on 23/Aug/24 $$\mathrm{If}\:\mathrm{only}\:\mathrm{the}\:\mathrm{result}\:\mathrm{is}\:\mathrm{accompanied}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{diagam}\:\mathrm{it}\:\mathrm{will}\:\mathrm{be}\:\mathrm{perfect}. \\ $$$${thanks}. \\ $$ Answered by…
Question Number 210940 by MrGHK last updated on 22/Aug/24 $$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{log}\left({x}\right){tanh}^{−\mathrm{1}} \left({x}\right){log}\left({x}^{\mathrm{2}} +\mathrm{1}\right)}{{x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210926 by maths_plus last updated on 22/Aug/24 $$\mathrm{valeur}\:\mathrm{de}\::\: \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{7}}\right)+\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{2}\pi}{\mathrm{7}}\right)+\mathrm{tan}^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{7}}\right)\:=\:??? \\ $$ Commented by mr W last updated on 22/Aug/24…
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Question Number 210933 by mnjuly1970 last updated on 22/Aug/24 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\mathrm{I}=\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}\:} \frac{\:{sin}\left(\:\mathrm{25}{x}\:\right)}{{sinx}}\:{dx}=? \\ $$$$ \\ $$$$ \\…