Question Number 210991 by Ismoiljon_008 last updated on 25/Aug/24 Commented by Ismoiljon_008 last updated on 25/Aug/24 $$\:\:\:{DC}=\mathrm{5} \\ $$ Commented by Ismoiljon_008 last updated on…
Question Number 210967 by mahdipoor last updated on 24/Aug/24 $${Q}.\mathrm{210956} \\ $$$${im}\:{read}\:{leithold}\:{book}\:{again}\:,\:{in}\:{this}\:{book}\:: \\ $$$$\left.\mathrm{1}\right\}{define}\::\:{ln}\left({x}\right)=\int_{\mathrm{1}} ^{\:{x}} {dx}/{x}\:\:\:\:\:\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{2}\right\}{define}\::\:{ln}\left({e}\right)=\mathrm{1}=\int_{\mathrm{1}} ^{\:{e}} {dx}/{x} \\ $$$$\left.\mathrm{3}\right\}{define}\::\:{exp}\left({x}\right)={y}\:\Leftrightarrow\:{ln}\left({y}\right)={x} \\ $$$$\frac{{d}\left({ln}\left({u}\right)\right)}{{du}}=\frac{\mathrm{1}}{{u}}\:\Rightarrow\:\frac{{d}\left({ln}\left({u}\right)\right)}{{dx}}=\frac{{du}/{dx}}{{u}}\:\Rightarrow \\…
Question Number 210956 by mahdipoor last updated on 23/Aug/24 $${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 $$\mathrm{an}\:\mathrm{idea}:…
Question Number 210940 by MrGHK last updated on 22/Aug/24 $$\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} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210920 by MrGHK last updated on 22/Aug/24 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210896 by MrGHK last updated on 21/Aug/24 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\overset{−} {{H}}_{{n}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)^{{q}} }=?? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 210782 by Ismoiljon_008 last updated on 19/Aug/24 $$ \\ $$$$\:\:\:\mathscr{H}{ow}\:{to}\:{make}\:\mathrm{4}\:{out}\:{of}\:{four}\:\:\mathrm{0}'{s}\:? \\ $$$$\:\:\:\mathscr{HELP}\:\mathscr{PLEASE} \\ $$$$ \\ $$ Commented by mr W last updated on…
Question Number 210839 by klipto last updated on 19/Aug/24 $$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\int_{\mathrm{0}} ^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{e}}^{\boldsymbol{\mathrm{xt}}} \boldsymbol{\mathrm{e}}^{−\mathrm{t}^{\mathrm{2}} } \boldsymbol{\mathrm{dt}}=\boldsymbol{\mathrm{e}}^{\frac{\boldsymbol{\mathrm{x}}^{\mathrm{2}} }{\mathrm{4}}} \underset{\mathrm{0}} {\int}^{\boldsymbol{\mathrm{x}}} \boldsymbol{\mathrm{e}}^{−\frac{\boldsymbol{\mathrm{t}}^{\mathrm{2}} }{\mathrm{4}}} \\ $$$$ \\ $$ Commented…
Question Number 210788 by liuxinnan last updated on 19/Aug/24 $${s}=\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\mathrm{2}^{{i}} \\ $$$$\mathrm{2}{s}={s}−\mathrm{1} \\ $$$${s}=\mathrm{1}\:? \\ $$$$\:{how}\:{to}\:{explain}\:{it} \\ $$$${and}\:{how}\:{to}\:{judge}\:{which}\:{case}\:{can}\:{use}\:{this}\:{way} \\ $$ Answered by Berbere…
Question Number 210754 by mokys last updated on 18/Aug/24 Answered by Berbere last updated on 19/Aug/24 $$\mathrm{1}+{N}^{{r}} \sim{N}^{{r}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\underset{{k}=\mathrm{1}} {\overset{{N}} {\sum}}{k}^{{s}} }{{N}^{{s}} }=\underset{{N}\rightarrow\infty}…