Question Number 36442 by abdo mathsup 649 cc last updated on 02/Jun/18 $${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{2}+{x}^{\mathrm{2}} \:}\:\:\:−{x} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right)\:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:\frac{{f}\left({x}\right)}{{x}}\:{and}\:\:{lim}_{{x}\rightarrow−\infty} \:\frac{{f}\left({x}\right)}{{x}} \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:{f}^{'} \left({x}\right)\:{and}\:{determine}\:{its}\:{sign}…
Question Number 36367 by chakraborty ankit last updated on 01/Jun/18 $$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$…
Question Number 36179 by prof Abdo imad last updated on 30/May/18 $${let}\:{f}\left({x},{y}\right)\:=\:\frac{{xy}}{{x}+{y}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right){calcule}\:{x}\frac{\partial{f}}{\partial{x}}\left({x},{y}\right)\:+{y}\:\frac{\partial{f}}{\partial{y}}\left({x},{y}\right)\:{interms}\:{of}\:{f}\left({x},{y}\right) \\ $$ Commented by maxmathsup by imad last updated…
Question Number 36104 by rahul 19 last updated on 28/May/18 $$\mathrm{If}\:\boldsymbol{\mathrm{f}}:\boldsymbol{\mathrm{R}}\rightarrow\boldsymbol{\mathrm{R}}\:\mathrm{is}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mid\:\mathrm{f}\left({x}\right)\:−\:\mathrm{f}\left(\mathrm{y}\right)\mid\:\leqslant\:\mid\:\mathrm{sin}\:{x}\:−\:\mathrm{sin}\:\mathrm{y}\:\mid\forall{x},\mathrm{y}\in\mathbb{R}, \\ $$$$\mathrm{Then}\:\mathrm{f}\left({x}\right)\:\mathrm{is}\: \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Bijective} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{many}−\mathrm{one} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{periodic} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{non}−\mathrm{periodic} \\ $$…
Question Number 101595 by mathmax by abdo last updated on 03/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{cos}^{\mathrm{n}} \mathrm{x} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{find}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{detemine}\:\:\int\:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Answered by…
Question Number 36010 by abdo mathsup 649 cc last updated on 27/May/18 $${let}\:{f}\left({x}\right)=\:\:\frac{{x}}{{x}^{\mathrm{2}} \:+{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by prof Abdo…
Question Number 35988 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({x}\right)\:=\:\frac{{x}+\mathrm{2}}{{x}^{\mathrm{3}} −\mathrm{4}{x}\:+\mathrm{3}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}. \\ $$ Commented by abdo mathsup…
Question Number 35986 by abdo mathsup 649 cc last updated on 26/May/18 $${let}\:{f}\left({x}\right)=\:\sqrt{\mathrm{1}\:+{n}\:{x}^{\mathrm{2}} }\:\:\:−{nx}\:+\mathrm{3}\:\:{with}\:{n}\:{integr} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \:{and}\:{lim}_{{x}\rightarrow−\infty} {f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{equation}\:{of}\:{assymptote}\:{of}\:{f}\:{at} \\ $$$${point}\:\:{A}\left(\mathrm{1},{f}\left(\mathrm{1}\right)\right)\:.…
Question Number 101500 by mathmax by abdo last updated on 03/Jul/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{cosx}\:.\mathrm{cos}\left(\mathrm{2x}\right).\mathrm{cos}\left(\mathrm{3x}\right) \\ $$$$\left.\mathrm{1}\right)\mathrm{calculate}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{x}\right)\:\mathrm{and}\:\mathrm{f}^{\left(\mathrm{n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\:\mathrm{integr}\:\mathrm{serie} \\ $$$$\mathrm{3}.\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\ $$ Commented…
Question Number 167003 by cortano1 last updated on 04/Mar/22 $$\:\:\:\:\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\mathrm{n}=\infty} {\sum}}\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{n}} \mathrm{cos}\:\left(\mathrm{180}°\mathrm{n}\right)=\:? \\ $$ Answered by greogoury55 last updated on 04/Mar/22 $$\:\mathrm{cos}\:\left(\mathrm{180}°{n}\right)=\left(−\mathrm{1}\right)^{{n}} \\ $$$$\:\underset{{n}=\mathrm{2}}…