Question Number 203158 by hardmath last updated on 11/Jan/24 $$\mathrm{1}.\:\mathrm{y}\:=\:\mathrm{tg}^{\mathrm{2}} \:\mathrm{x}\:\:\:\Rightarrow\:\:\:\mathrm{y}^{'} \:=\:? \\ $$$$\mathrm{2}.\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\:\left(\mathrm{1}\:+\:\mathrm{2x}\right)}{\mathrm{sin}\:\mathrm{2x}}\:=\:? \\ $$ Answered by shunmisaki007 last updated on 11/Jan/24 $$\mathrm{1}.\:\mathrm{Are}\:{t},\:{g},\:\mathrm{and}\:{x}\:\mathrm{all}\:\mathrm{variable}\:\mathrm{or}\:\mathrm{one}\:\mathrm{or}\:\mathrm{two}\:\mathrm{of}\:\mathrm{them}\:\mathrm{constant}?…
Question Number 203149 by hardmath last updated on 11/Jan/24 $$\mathrm{If}\:\:\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:=\:\mathrm{2} \\ $$$$\mathrm{Then}\:\:\:\sqrt{\mathrm{2a}\:+\:\mathrm{7}}\:+\:\sqrt{\mathrm{2b}\:+\:\mathrm{7}}\:\leqslant\:\mathrm{6} \\ $$ Commented by mr W last updated on 12/Jan/24 $$\underset{{a}={b}=−\mathrm{1}}…
Question Number 203144 by mustafazaheen last updated on 11/Jan/24 $$\mathrm{when}\:\:\:\:\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{sinx}\:\:\:\:\:\pi<\mathrm{x}\leqslant\mathrm{2}\pi}\\{\mathrm{cosx}\:\:\:\:\:\frac{\pi}{\mathrm{2}}\leqslant\mathrm{x}\leqslant\pi}\end{cases}\:\:\:\:\:\:\:\:\mathrm{find}\:\:{f}'\left(\mathrm{2}\pi\right)=? \\ $$ Commented by mr W last updated on 13/Jan/24 $$\mathrm{f}'\left(\mathrm{2}\pi\right)\:{doesn}'{t}\:{exist},\:{since}\:{f}\left({x}\right)\:{is}\:{not} \\ $$$${defined}\:{for}\:{x}>\mathrm{2}\pi. \\ $$…
Question Number 203169 by hardmath last updated on 11/Jan/24 $$\mathrm{If}\:\:\:\mathrm{y}\:=\:\mathrm{tan} \\ $$$$\mathrm{Find}\:\:\:\mathrm{y}^{'} \:=\:? \\ $$ Answered by a.lgnaoui last updated on 11/Jan/24 $$\mathrm{y}'=\frac{\mathrm{cos}^{\mathrm{2}} +\mathrm{sin}\:^{\mathrm{2}} }{\mathrm{cos}\:^{\mathrm{2}}…
Question Number 203066 by mathlove last updated on 09/Jan/24 $${if}\:{p}=\frac{{x}^{\mathrm{2}} }{{x}−\mathrm{2}}−\frac{{x}}{\mathrm{1}+\frac{\mathrm{2}}{{x}}}−\frac{\mathrm{4}}{\mathrm{1}+\frac{\mathrm{4}}{{x}^{\mathrm{2}} }}\:\:\:{and}\:{x}−\frac{\mathrm{4}}{{x}}=\mathrm{2} \\ $$$${then}\:{show}\:{that}\:\:\left(\frac{\mathrm{32}}{{p}}\right)^{\mathrm{2}} =\mathrm{80} \\ $$ Answered by Rasheed.Sindhi last updated on 09/Jan/24 $${if}\:{p}=\frac{{x}^{\mathrm{2}}…
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Question Number 203061 by York12 last updated on 08/Jan/24 $$\mathrm{14}\int\frac{\mathrm{1}}{\mathrm{x}\left[\mathrm{ln}\left(\mathrm{x}\right)\right]^{\mathrm{3}} \:}\:\:\mathrm{d}\left(\mathrm{x}\right) \\ $$ Answered by MM42 last updated on 09/Jan/24 $${ans} \\ $$$$\:\frac{−\mathrm{7}}{\left({lnx}\right)^{\mathrm{2}} } \\…
Question Number 203002 by mr W last updated on 07/Jan/24 $${Solve}\:{for}\:{x}\in{R} \\ $$$${x}^{\mathrm{4}} +\mathrm{4}{x}−\mathrm{3}=\mathrm{0} \\ $$ Answered by ajfour last updated on 07/Jan/24 $${p}^{\mathrm{2}} \left({p}^{\mathrm{4}}…
Question Number 203035 by Frix last updated on 07/Jan/24 $$\mathrm{e}=\mathrm{2} \\ $$$$\mathrm{Proof}: \\ $$$$\mathrm{Let}\:{x}=\frac{\mathrm{e}+\mathrm{2}}{\mathrm{2}} \\ $$$$\mathrm{2}{x}=\mathrm{e}+\mathrm{2} \\ $$$$\mathrm{2}{x}\left(\mathrm{e}−\mathrm{2}\right)=\left(\mathrm{e}+\mathrm{2}\right)\left(\mathrm{e}−\mathrm{2}\right) \\ $$$$\mathrm{2e}{x}−\mathrm{4}{x}=\mathrm{e}^{\mathrm{2}} −\mathrm{4} \\ $$$$−\mathrm{4}{x}+\mathrm{4}=−\mathrm{2e}{x}+\mathrm{e}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}}…
Question Number 203011 by esmaeil last updated on 07/Jan/24 $$\int\frac{{u}}{{du}}=? \\ $$$${Is}\:{this}\:{question}\:{correct}? \\ $$ Commented by mr W last updated on 07/Jan/24 $${just}\:{non}−{sense}. \\ $$…