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Category: Differentiation

If-x-y-gt-1-Min-x-4-y-1-2-y-4-x-1-2-m-n-

Question Number 151942 by mnjuly1970 last updated on 24/Aug/21 $$ \\ $$$$\:\:\:\mathrm{If}\:\:{x}\:,\:{y}\:>\:\mathrm{1}\:\:\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Min}\:\left(\:\frac{\:{x}^{\:\mathrm{4}} }{\left({y}\:−\mathrm{1}\:\right)^{\:\mathrm{2}} }\:+\:\frac{\:{y}^{\:\mathrm{4}} }{\left(\:{x}\:−\:\mathrm{1}\:\right)^{\:\mathrm{2}} }\:\right)\:=\:?\:……\blacksquare\:\:?\:\: \\ $$$$\:\:\:\:{m}.{n}… \\ $$$$ \\…

The-time-period-T-of-pendulum-of-length-l-is-given-by-T-2-l-g-where-l-amd-g-are-constant-Find-the-approximate-percentage-increase-in-time-T-when-the-length-of-pendulum-increases-by-4-

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…

the-rectangle-is-known-to-be-twice-as-long-as-its-wide-if-the-width-is-measured-as-20-0-2cm-find-the-area-in-the-form-of-A-b-

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…

1-prove-that-0-e-t-ln-t-1-e-t-2-dt-1-2-ln-pi-2-

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…