Question Number 227073 by Spillover last updated on 29/Dec/25 Answered by Kassista last updated on 29/Dec/25 $$ \\ $$$$\frac{{dy}}{{dx}}=\:\frac{−\left({x}−{b}\right)+\left({a}−{x}\right)}{\mathrm{2}\sqrt{\left({a}−{x}\right)\left({x}−{b}\right)}}−\left({a}−{b}\right).\frac{\mathrm{1}}{\mathrm{1}+\left(\sqrt{\frac{{a}−{x}}{{x}−{b}}}\right)^{\mathrm{2}} }.\frac{\frac{−\left({x}−{b}\right)−\left({a}−{x}\right)}{\left({x}−{b}\right)^{\mathrm{2}} }}{\mathrm{2}\sqrt{\frac{{a}−{x}}{{x}−{b}}}} \\ $$$$ \\ $$$$…
Question Number 227054 by Spillover last updated on 28/Dec/25 $${A}\:{Segment}\:{of}\:{a}\:{sphere}\:{has}\:{radius}\:{r} \\ $$$${and}\:{maximum}\:{height}\:{h}.{Prove}\:{that} \\ $$$${its}\:{volume}\:\frac{\boldsymbol{\pi{h}}}{\mathrm{6}}\left(\boldsymbol{{h}}^{\mathrm{2}} +\mathrm{3}\boldsymbol{{r}}^{\mathrm{2}} \right) \\ $$ Answered by fantastic2 last updated on 29/Dec/25…
Question Number 226820 by Spillover last updated on 16/Dec/25 $$ \\ $$$$\:\:\:\:\:{Differentiate}\:\:\:\:{x}^{{x}^{{x}} } \\ $$$$ \\ $$ Answered by AgniMath last updated on 16/Dec/25 $${y}={x}^{{x}^{{x}}…
Question Number 226821 by Spillover last updated on 16/Dec/25 $${Differentiate}\:\: \\ $$$$\mathrm{20sin}\:\left({x}+\mathrm{3}\right)\mathrm{cos}\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}} \\ $$ Answered by AgniMath last updated on 16/Dec/25 $$\frac{{d}}{{dx}}\:{sin}\left({x}+\mathrm{3}\right)\:=\:{cos}\left({x}+\mathrm{3}\right) \\ $$$$\frac{{d}}{{dx}}\:{cos}\frac{{x}^{\mathrm{2}}…
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Question Number 225047 by fantastic last updated on 16/Oct/25 $$\int\:{x}^{{x}} \:{dx} \\ $$ Answered by Ghisom_ last updated on 16/Oct/25 $$\mathrm{impossible} \\ $$ Commented by…
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Question Number 223006 by mnjuly1970 last updated on 12/Jul/25 $$ \\ $$$$\:\:\:\:\:\:\:\:\mathscr{L}\:\:\left\{\:{tsin}\left(\sqrt{{t}}\:\right)\right\}=? \\ $$ Answered by MrGaster last updated on 12/Jul/25 $$\mathscr{L}\:\:\left\{\:{tsin}\left(\sqrt{{t}}\:\right)\right\}=\int_{\mathrm{0}} ^{\infty} {e}^{−{st}} {t}\:\mathrm{sin}\left(\sqrt{{t}}\right){dt}…
Question Number 222778 by Osefavour last updated on 07/Jul/25 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2log}\left(\mathrm{1}+\mathrm{x}\right)−\frac{\mathrm{x}\left(\mathrm{3x}+\mathrm{2}\right)}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} }}{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by MrGaster last updated on 09/Jul/25 $$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{2}\left({x}−\frac{{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{{x}^{\mathrm{3}}…