Question Number 98398 by bemath last updated on 13/Jun/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+…}}}}} \\ $$$$\mathrm{f}\:'\left(\mathrm{5}\right)\:=\: \\ $$ Commented by bobhans last updated on 14/Jun/20 $$\mathrm{let}\:\mathrm{y}\:=\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{\mathrm{x}+\sqrt{…}}}}} \\ $$$$\mathrm{defined}\:\mathrm{for}\:\begin{cases}{\mathrm{x}\geqslant\mathrm{0}}\\{\mathrm{y}\geqslant\mathrm{0}}\end{cases} \\…
Question Number 163928 by mathlove last updated on 12/Jan/22 $${f}\left({x}\right)=\frac{\mathrm{2}{x}^{\mathrm{100}!} }{\mathrm{100}!}+{x}^{\mathrm{100}} +\mathrm{1} \\ $$$${find}\:\:\:\frac{{d}^{\mathrm{100}!} {f}\left({x}\right)}{{dx}^{\mathrm{100}!} }=? \\ $$ Answered by mr W last updated on…
Question Number 32776 by NECx last updated on 02/Apr/18 $${Find}\:{the}\:{optimum}\:{points}\:{of} \\ $$$${the}\:{function}\:{y}={f}\left({x}\right) \\ $$$$\:\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{36}{x}+\mathrm{34} \\ $$ Answered by MJS last updated on 02/Apr/18…
Question Number 32775 by NECx last updated on 02/Apr/18 $${Find}\:{the}\:{area}\:{bounded}\:{by}\:{the} \\ $$$${curve}\:{y}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3},{the}\:{x}\:{axis} \\ $$$${and}\:{the}\:{line}\:{x}=\mathrm{5}\:{and}\:{x}=\mathrm{2} \\ $$ Answered by MJS last updated on 02/Apr/18 $$\mathrm{1}.\:\mathrm{check}\:\mathrm{the}\:\mathrm{zeros}…
Question Number 32756 by NECx last updated on 01/Apr/18 $${Please}\:{help} \\ $$$$ \\ $$$${Find}\:{the}\:{area}\:{bounded}\:{by} \\ $$$${y}\left({x}+\mathrm{2}\right)={x}^{\mathrm{4}} ,{x}=\mathrm{0},{y}=\mathrm{0},{and}\:{x}=\mathrm{3} \\ $$ Answered by MJS last updated on…
Question Number 98244 by ~blr237~ last updated on 12/Jun/20 $$\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:{xe}^{{cosx}} {cos}\left({sinx}\right){dx}=\:\mathrm{2}\pi^{\mathrm{2}} \\ $$ Answered by maths mind last updated on 15/Jun/20 $${e}^{{cos}\left({x}\right)+{isin}\left({x}\right)} ={e}^{{cos}\left({x}\right)}…
Question Number 98213 by me2love2math last updated on 12/Jun/20 Commented by bemath last updated on 12/Jun/20 $$\mathrm{let}\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{t}\:,\:\mathrm{t}\:\rightarrow\mathrm{0}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{3}{t}\right)}{{t}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3t}}}{\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{3} \\ $$ Answered by…
Question Number 163732 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$ Terms of…
Question Number 163704 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\:\Omega=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{n}\left(\zeta\:\left(\mathrm{1}+{n}\right)\:−\mathrm{1}\right)\:=? \\ $$$$ \\ $$ Answered by Kamel last updated…
Question Number 163700 by blackmamba last updated on 09/Jan/22 $$\:\:\mathcal{K}\left({x}\right)\:=\:\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4sin}\:{x}} \\ $$$$\:\left.\begin{matrix}{{max}\:\mathcal{K}\left({x}\right)}\\{{min}\:\mathcal{K}\left({x}\right)}\end{matrix}\right\}\:=? \\ $$ Answered by mr W last updated on 10/Jan/22 $$\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4}\:\mathrm{sin}\:{x}}={k} \\ $$$$\mathrm{3}\:\mathrm{cos}\:{x}−\mathrm{4}{k}\:\mathrm{sin}\:{x}=\mathrm{5}{k}…