Question Number 193328 by mustafazaheen last updated on 10/Jun/23 $$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\frac{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}}\:;\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{1}}\\{\mathrm{2x}+\mathrm{1};\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{1}}\end{cases} \\ $$$$\mathrm{thene}\:\mathrm{find}\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}{f}\left({x}\right)=? \\ $$ Answered by cortano12 last updated on 10/Jun/23 $$\:\:\underset{{x}\rightarrow\mathrm{1}}…
Question Number 193236 by Mingma last updated on 08/Jun/23 Answered by MM42 last updated on 09/Jun/23 $${if}\:\:“{p}''\:{is}\:{prime}\:{number}\:\Rightarrow\:\left({p}−\mathrm{1}\right)!\overset{{p}} {\equiv}−\mathrm{1}\:\:\left({wilson}'{d}\:{theorem}\right) \\ $$$${h}=\mathrm{17}{k}+\mathrm{5}\Rightarrow{h}\overset{\mathrm{17}} {\equiv}\:\mathrm{5}\:\: \\ $$ Answered by…
Question Number 193248 by mnjuly1970 last updated on 08/Jun/23 $$ \\ $$$$\:\mathrm{L}=\:\mathrm{lim}_{\:{x}\rightarrow\mathrm{0}} \:\frac{\:\mathrm{sin}\left({x}\:\right)−\mathrm{arcsin}\left({x}\right)}{\mathrm{tan}\left({x}\right)−\:\mathrm{arctan}\left({x}\right)}=?\:\:\:\:\:\:\: \\ $$$$ \\ $$$$\:\:\:\: \\ $$ Answered by MM42 last updated on…
Question Number 193117 by mustafazaheen last updated on 04/Jun/23 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{cosx}\right)^{\frac{\mathrm{1}}{\mathrm{x}}} \\ $$ Answered by Subhi last updated on 04/Jun/23 $${y}\:=\:{lim}_{{x}\rightarrow\mathrm{0}} \:\left({cosx}\right)^{\frac{\mathrm{1}}{{x}}} \\ $$$${ln}\left({y}\right)\:=\:{lim}_{{x}\rightarrow\mathrm{0}} \:\frac{{ln}\left({cosx}\right)}{{x}}…
Question Number 131052 by benjo_mathlover last updated on 01/Feb/21 $$\:\underset{{x}\rightarrow{s}} {\mathrm{lim}}\:\frac{{x}^{{s}^{{s}} } −{s}^{{x}^{{s}} } }{{x}^{\mathrm{2}} −{s}^{\mathrm{2}} }\:=? \\ $$ Answered by Ar Brandon last updated…
Question Number 131033 by greg_ed last updated on 31/Jan/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}−\mathrm{tan}\:{x}}{{x}\:\mathrm{tan}^{\mathrm{2}} {x}}\:=\:? \\ $$ Commented by greg_ed last updated on 02/Feb/21 $$\boldsymbol{\mathrm{without}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{limited}}\:\boldsymbol{\mathrm{development}}\:\boldsymbol{\mathrm{method}}\:! \\ $$ Answered…
Question Number 65490 by Masumsiddiqui399@gmail.com last updated on 30/Jul/19 Commented by mathmax by abdo last updated on 31/Jul/19 $${hospital}\:{method}\:\:{let}\:{u}\left({x}\right)\:={ln}\left({x}\right)\:{and}\:{v}\left({x}\right)={cos}\left(\frac{\pi}{\mathrm{2}^{{x}} }\right) \\ $$$${we}\:{have}\:{lim}_{{x}\rightarrow\mathrm{1}} {u}\left({x}\right)={lim}_{{x}\rightarrow\mathrm{1}} {v}\left({x}\right)\:=\mathrm{0} \\…
Question Number 65472 by Masumsiddiqui399@gmail.com last updated on 30/Jul/19 $$ \\ $$$$ \\ $$$$\:\:\:{solve}\:\: \\ $$$$\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left[\left(\mathrm{2}+{x}\right)^{{n}} −\mathrm{2}^{{n}} \right]}{{x}} \\ $$$$ \\ $$ Commented by…
Question Number 65473 by Tawa1 last updated on 30/Jul/19 Commented by mathmax by abdo last updated on 30/Jul/19 $${let}\:\:{A}\left({x}\right)\:=\sqrt{\frac{{x}^{\mathrm{3}} −\mathrm{1}}{{x}+\mathrm{1}}}−^{\mathrm{3}} \sqrt{\frac{{x}^{\mathrm{5}} +\mathrm{1}}{{x}^{\mathrm{2}} −\mathrm{2}{x}}}\:\Rightarrow{for}\:{x}>\mathrm{0} \\ $$$${A}\left({x}\right)\:=\sqrt{\frac{{x}^{\mathrm{3}}…
Question Number 65464 by aliesam last updated on 30/Jul/19 Commented by mathmax by abdo last updated on 30/Jul/19 $${let}\:\:{A}\left({x}\right)\:={x}\left({x}+\mathrm{1}\right){ln}\left(\frac{{x}+\mathrm{1}}{{x}}\right)−{x}\:\:\:\:{we}\:{have}\:{for}\:{x}\in{V}\left(+\infty\right) \\ $$$${ln}\left(\frac{{x}+\mathrm{1}}{{x}}\right)\:={ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)\:=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\:+{o}\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\: \\ $$$${A}\left({x}\right)\:=\left({x}^{\mathrm{2}}…