Question Number 151942 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:\mathrm{If}\:\:{x}\:,\:{y}\:>\:\mathrm{1}\:\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\frac{\:{x}^{\:\mathrm{4}} }{\left({y}\:−\mathrm{1}\:\right)^{\:\mathrm{2}} }\:+\:\frac{\:{y}^{\:\mathrm{4}} }{\left(\:{x}\:−\:\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:?\:……\blacksquare\:\:?\:\: \\ $$$$\:\:\:\:{m}.{n}… \\ $$$$ \\…
Question Number 20850 by j.masanja06@gmail.com last updated on 04/Sep/17 $${given}\:{that}\:{y}={log}\sqrt{\frac{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{\mathrm{1}−{e}^{\mathrm{2}{x}} }},{find} \\ $$$$\frac{{dy}}{{dx}} \\ $$ Answered by Hitler last updated on 05/Sep/17 $$\frac{−{sinxcosx}+\left(\mathrm{1}+{sinxcosx}+{cos}^{\mathrm{2}} {x}\right){e}^{\mathrm{2}{x}}…
Question Number 20851 by j.masanja06@gmail.com last updated on 04/Sep/17 $${if}\:\left({x}+{y}\right)^{{m}+{n}} ={x}^{{m}} {y}^{{n}} ,{show}\:{that}\:\frac{{dy}}{{dx}}=\frac{{y}}{{x}} \\ $$ Answered by ajfour last updated on 04/Sep/17 $${taking}\:{logarithm}\:{on}\:{both}\:{sides}: \\ $$$$\left({m}+{n}\right)\mathrm{ln}\:\left({x}+{y}\right)={m}\mathrm{ln}\:{x}+{n}\mathrm{ln}\:{y}…
Question Number 20849 by j.masanja06@gmail.com last updated on 04/Sep/17 $${The}\:{time}\:{period},{T}\:\:{of}\:{pendulum}\:{of} \\ $$$${length}\:{l}\:{is}\:{given}\:{by}\:{T}=\mathrm{2}\Pi\sqrt{\frac{{l}}{{g}}}{where} \\ $$$$\:{l}\:{amd}\:{g}\:{are}\:{constant}.{Find}\:{the}\: \\ $$$${approximate}\:{percentage}\:{increase}\: \\ $$$${in}\:{time}\:{T},\:{when}\:{the}\:{length}\:{of}\: \\ $$$${pendulum}\:{increases}\:{by}\:\mathrm{4\%} \\ $$ Answered by mrW1…
Question Number 20847 by j.masanja06@gmail.com last updated on 04/Sep/17 $${the}\:{rectangle}\:{is}\:{known}\:{to}\:{be}\:{twice} \\ $$$${as}\:{long}\:{as}\:{its}\:{wide}.{if}\:{the}\:{width}\:{is} \\ $$$${measured}\:{as}\:\mathrm{20}\:\pm\mathrm{0}.\mathrm{2}{cm}. \\ $$$${find}\:{the}\:{area}\:{in}\:{the}\:{form}\:{of}\:\left({A}\pm{b}\right) \\ $$$$ \\ $$ Answered by ajfour last updated…
Question Number 20831 by j.masanja06@gmail.com last updated on 04/Sep/17 $${if}\:{x}\sqrt{\mathrm{1}+{y}}\:+\:{y}\sqrt{\mathrm{1}+{x}}=\mathrm{0}\:{prove}\:{that}\: \\ $$$$\frac{{dy}}{{dx}}=−\left(\mathrm{1}+{x}\right)^{−\mathrm{2}} \\ $$ Answered by ajfour last updated on 04/Sep/17 $${x}\sqrt{\mathrm{1}+{y}}\:=−{y}\sqrt{\mathrm{1}+{x}}\: \\ $$$${so} \\…
Question Number 20832 by j.masanja06@gmail.com last updated on 04/Sep/17 $${Given}\:{that}\:{y}={log}\sqrt{\frac{\mathrm{1}−{cos}^{\mathrm{2}} {x}}{\mathrm{1}−{e}^{\mathrm{2}{x}} }} \\ $$$${find}\:\frac{{dy}}{{dx}} \\ $$ Commented by myintkhaing last updated on 04/Sep/17 $$\mathrm{ecos}^{\mathrm{2}} \mathrm{x}\:???…
Question Number 86288 by john santu last updated on 28/Mar/20 $$\int\:\:\frac{{dx}}{\left(\mathrm{1}+{x}^{\mathrm{4}} \right)^{\mathrm{1}/\mathrm{4}} } \\ $$ Answered by TANMAY PANACEA. last updated on 28/Mar/20 $${x}^{\mathrm{2}} ={tana}…
Question Number 151819 by mnjuly1970 last updated on 23/Aug/21 $$ \\ $$$$\:\:\:\:\:\mathrm{1}.\:{prove}\:{that}\:: \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \frac{\:{e}^{\:{t}} .{ln}\left({t}\:\right)}{\left(\mathrm{1}\:+\:{e}^{\:{t}} \right)^{\:\mathrm{2}} }\:{dt}=\frac{\mathrm{1}}{\mathrm{2}}\left({ln}\left(\frac{\pi}{\mathrm{2}}\:\right)−\:\gamma\:\right)\: \\ $$$$\:\:\: \\ $$ Answered by…
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