Question Number 79879 by TawaTawa last updated on 28/Jan/20 Commented by TawaTawa last updated on 29/Jan/20 $$\mathrm{Please}\:\mathrm{help}. \\ $$ Commented by john santu last updated…
Question Number 145390 by puissant last updated on 04/Jul/21 $$\varphi\left(\mathrm{x}\right)=\mathrm{ln}\left(\frac{\mathrm{e}^{\mathrm{x}+\mathrm{cos}\left(\mathrm{x}\right)} −\mathrm{e}}{\mathrm{x}+\mathrm{x}^{\mathrm{2}} }\right) \\ $$$$\mathrm{montrer}\:\mathrm{que}\:\varphi\:\mathrm{se}\:\mathrm{prolonge}\:\mathrm{par}\:\mathrm{continuit}\acute {\mathrm{e}} \\ $$$$\mathrm{en}\:\mathrm{0}.\:\mathrm{on}\:\mathrm{note}\:\psi\:\mathrm{son}\:\mathrm{prolongement},\:\mathrm{montrer} \\ $$$$\mathrm{que}\:\psi\:\mathrm{est}\:\mathrm{d}\acute {\mathrm{e}rivable}\:\mathrm{en}\:\mathrm{0}..\:\:\mathrm{Ainsi}\:\mathrm{donner}\:\mathrm{une} \\ $$$$\acute {\mathrm{e}quation}\:\mathrm{de}\:\mathrm{la}\:\mathrm{tangente},\:\mathrm{position}\:\mathrm{de}\:\mathrm{la}\:\mathrm{courbe} \\ $$$$\mathrm{par}\:\mathrm{rapport}\:\mathrm{a}\:\mathrm{la}\:\mathrm{tangente},\:\mathrm{et}\:\mathrm{faire}\:\mathrm{le}\:\mathrm{dessin}..…
Question Number 145391 by puissant last updated on 04/Jul/21 $$\mathrm{Developpement}\:\mathrm{limit}\acute {\mathrm{e}}\:\mathrm{a}\:\mathrm{l}'\mathrm{ordre}\:\mathrm{2}\:\mathrm{de}\: \\ $$$$\mathrm{g}\left(\mathrm{x}\right)=\frac{\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }}{\mathrm{1}+\mathrm{x}+\sqrt{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }} \\ $$ Answered by Olaf_Thorendsen last updated on 04/Jul/21 $${g}\left({x}\right)\:=\:\frac{\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 79816 by jagoll last updated on 28/Jan/20 $$\mathrm{hello}\:\mathrm{mister}. \\ $$$$\mathrm{i}\:\mathrm{need}\:\mathrm{help}\:\mathrm{explaining}\:\mathrm{how}\:\mathrm{determine} \\ $$$$\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{of}\:\mathrm{rational}\:\mathrm{functions} \\ $$$$\mathrm{like}\:\left(\mathrm{i}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}^{\mathrm{2}} +\mathrm{qx}+\mathrm{r}} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}}{\mathrm{px}+\mathrm{q}} \\ $$…
Question Number 145338 by puissant last updated on 04/Jul/21 $$\mathrm{d}\acute {\mathrm{e}riv}\acute {\mathrm{e}e}\:\:\:\mathrm{n}-\mathrm{i}\grave {\mathrm{e}me}\:\:\:\mathrm{de}\:\:\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{1}+\mathrm{x}^{\mathrm{6}} } \\ $$ Answered by mathmax by abdo last updated on…
Question Number 79756 by mathmax by abdo last updated on 27/Jan/20 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{1}} \:\:\frac{{sin}\left(\pi{x}\right)}{\mathrm{1}−{x}^{\mathrm{2}} }\:\:{without}\:{hospital}\:{rule} \\ $$ Commented by john santu last updated on 27/Jan/20 $$\underset{{x}\rightarrow\mathrm{1}}…
Question Number 145294 by imjagoll last updated on 04/Jul/21 $$\mathrm{Given}\:\mathrm{a}\:\mathrm{polynomial}\: \\ $$$$\mathrm{p}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{4}} +\mathrm{4x}^{\mathrm{3}} +\left(\mathrm{2p}+\mathrm{2}\right)\mathrm{x}^{\mathrm{2}} +\left(\mathrm{2p}+\mathrm{5q}+\mathrm{2}\right)\mathrm{x}+\mathrm{3q}+\mathrm{2r}. \\ $$$$\mathrm{If}\:\mathrm{p}\left(\mathrm{x}\right)=\:\left(\mathrm{x}^{\mathrm{3}} +\mathrm{2x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{6}\right)\mathrm{Q}\left(\mathrm{x}\right) \\ $$$$\:\mathrm{then}\:\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\left(\mathrm{p}+\mathrm{2q}\right)\mathrm{r}\:. \\ $$…
Question Number 145165 by mathmax by abdo last updated on 02/Jul/21 $$\mathrm{calculate}\:\:\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \mathrm{arctan}\left(\frac{\mathrm{2n}+\mathrm{1}}{\mathrm{n}^{\mathrm{4}} \:+\mathrm{2n}^{\mathrm{3}} \:+\mathrm{n}^{\mathrm{2}} \:+\mathrm{1}}\right) \\ $$ Answered by mnjuly1970 last updated on…
Question Number 145119 by imjagoll last updated on 02/Jul/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{5}\right)} }{\mathrm{3}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{3}\right)} }\:=?\: \\ $$ Answered by Rasheed.Sindhi last updated on 03/Jul/21 $$\:\frac{\mathrm{5}^{\mathrm{log}\:_{\frac{\mathrm{5}}{\mathrm{3}}} \left(\mathrm{5}\right)}…
Question Number 145000 by imjagoll last updated on 01/Jul/21 $$\mathrm{If}\:\mathrm{F}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{F}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{then}\:\mathrm{F}^{−\mathrm{1}} \left(\mathrm{x}\right)=? \\ $$ Commented by prakash jain last updated on 01/Jul/21 $${f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right)^{\mathrm{2}}…