Question Number 65387 by mathmax by abdo last updated on 29/Jul/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{arctan}\left(\mathrm{2}{x}\right)−{arctanx}}{{x}}{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65386 by mathmax by abdo last updated on 29/Jul/19 $${calculate}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{\mathrm{99}{k}−\mathrm{1}} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 130921 by pticantor last updated on 30/Jan/21 $$\boldsymbol{{let}}\:\boldsymbol{{q}}\in\mathbb{R}/\:\mid\boldsymbol{{q}}\mid<\mathrm{1} \\ $$$$\: \\ $$$$\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{+\infty} {\sum}}\boldsymbol{{k}}^{\mathrm{2}} \boldsymbol{{q}}^{\boldsymbol{{k}}} =\frac{\boldsymbol{{q}}^{\mathrm{2}} +\boldsymbol{{q}}}{\left(\mathrm{1}−\boldsymbol{{q}}\right)^{\mathrm{3}} } \\ $$ Answered…
Question Number 130918 by bramlexs22 last updated on 30/Jan/21 $$\:\begin{cases}{{y}=\mathrm{sin}\:\theta−\mathrm{cos}\:^{\mathrm{3}} \theta}\\{{x}=\mathrm{cos}\:\theta−\mathrm{sin}\:^{\mathrm{3}} \theta}\end{cases} \\ $$$$\:\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:=? \\ $$ Answered by benjo_mathlover last updated on 30/Jan/21…
Question Number 65383 by mathmax by abdo last updated on 29/Jul/19 $$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\mathrm{1}+{e}^{{nx}} }\:\:\:{with}\:{n}\:{integr}\:{natural}\:\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{k}−\mathrm{1}} }{{k}} \\ $$ Commented by mathmax…
Question Number 65380 by ajfour last updated on 29/Jul/19 Commented by ajfour last updated on 29/Jul/19 $${Find}\:{radius}\:{r}\:{of}\:{a}\:{circle}\:{whose} \\ $$$${center}\:{is}\:{on}\:{the}\:{circumference} \\ $$$${of}\:{the}\:{unit}\:{circle}\:{and}\:{whose} \\ $$$${arc}\:{length}\:{within}\:{the}\:{shown} \\ $$$${unit}\:{radius}\:{circle}\:{is}\:{a}\:{maximum}.…
Question Number 130912 by Dwaipayan Shikari last updated on 30/Jan/21 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sech}\left({n}\pi\right)}{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65372 by aliesam last updated on 29/Jul/19 $${I}=\int_{\mathrm{1}} ^{{e}} \:\frac{{dx}}{{x}\left(\mathrm{1}+{ln}^{\mathrm{2}} {x}\right)} \\ $$ Commented by Prithwish sen last updated on 29/Jul/19 $$\mathrm{put}\:\mathrm{lnx}=\mathrm{tan}\theta\Rightarrow\frac{\mathrm{dx}}{\mathrm{x}}=\mathrm{sec}^{\mathrm{2}} \theta\mathrm{d}\theta…
Question Number 130907 by greg_ed last updated on 30/Jan/21 $$\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}+{x}^{\mathrm{2}} \right)}{{x}}\:{dx} \\ $$ Commented by benjo_mathlover last updated on 30/Jan/21 այս հարցն արդեն պատասխանվել է Commented by…
Question Number 65367 by ajfour last updated on 29/Jul/19 Commented by ajfour last updated on 29/Jul/19 $$\mathrm{For}\:\mathrm{maximum}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{origin}\:\mathrm{centered}\:\mathrm{circle}\:\mathrm{within} \\ $$$$\mathrm{the}\:\mathrm{shown}\:\mathrm{unit}\:\mathrm{circle},\:\mathrm{what}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{circle}. \\ $$…