Question Number 51984 by maxmathsup by imad last updated on 01/Jan/19 $$\left.\mathrm{1}\right)\:{prove}\:{the}\:{convexity}\:{of}\:{f}\left({x}\right)={ln}\left(\mathrm{1}+{e}^{{x}} \right) \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\left({x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,…,{x}_{{n}} \right)\in{R}^{{n}} \\ $$$$\mathrm{1}+\prod_{{k}=\mathrm{1}} ^{{n}} \left({x}_{{k}} \right)^{\frac{\mathrm{1}}{{n}}} \:\leqslant\:\prod_{{k}=\mathrm{1}} ^{{n}}…
Question Number 117518 by bobhans last updated on 12/Oct/20 $$\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{xf}\left(\mathrm{1}−\mathrm{x}\right)=\mathrm{x}^{\mathrm{2}} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=? \\ $$ Answered by bemath last updated on 12/Oct/20 $$\mathrm{replace}\:\mathrm{x}+\mathrm{1}\:\mathrm{by}\:\mathrm{x} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{f}\left(\mathrm{x}\right)+\left(\mathrm{x}−\mathrm{1}\right)\mathrm{f}\left(\mathrm{1}−\left(\mathrm{x}−\mathrm{1}\right)\right)=\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}}…
Question Number 51982 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:{u}_{{n}+\mathrm{1}} =\sqrt{\sum_{{k}=\mathrm{1}} ^{{n}} \:{u}_{{k}} }\:\:\:\:\:\:\:{with}\:{n}>\mathrm{0}\:\:\:{and}\:{u}_{\mathrm{1}} =\mathrm{1} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{\mathrm{2}} ,{u}_{\mathrm{3}} ,{u}_{\mathrm{4}} {and}\:{u}_{\mathrm{5}} \\ $$$$\left.\mathrm{2}\right){prove}\:{that}\:\:\forall{n}\geqslant\mathrm{2}\:\:\:\:\:{u}_{{n}+} ^{\mathrm{2}}…
Question Number 51983 by maxmathsup by imad last updated on 01/Jan/19 $${f}\:{is}\:{a}\:{real}\:{function}\:{derivable}\:{at}\:\mathrm{0}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{find} \\ $$$${lim}_{{n}\rightarrow+\infty} \sum_{{k}=\mathrm{1}} ^{{n}} \:{f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:. \\ $$ Terms of Service Privacy Policy…
Question Number 51981 by maxmathsup by imad last updated on 01/Jan/19 $${let}\:\:{U}_{{n}} =\:\frac{\sum_{{k}=\mathrm{1}} ^{{n}} \left[{lnk}\right]}{{ln}\left({n}!\right)}\:\:{determine}\:{lim}_{{n}\rightarrow+\infty} \:{U}_{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 117508 by bemath last updated on 12/Oct/20 $$\mathrm{f}\left(\mathrm{x}+\mathrm{1}\right)+\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)\:=\:\mathrm{x}^{\mathrm{2}} \: \\ $$$$\mathrm{find}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)\:=? \\ $$ Answered by bobhans last updated on 12/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{ax}^{\mathrm{2}} +\mathrm{bx}+\mathrm{c}…
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Question Number 117250 by mathmax by abdo last updated on 10/Oct/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{0}} \:\:\:\frac{\mathrm{sin}\left(\mathrm{xsh}\left(\mathrm{2x}\right)\right)−\mathrm{sh}\left(\mathrm{x}\:\mathrm{sin}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{3}} } \\ $$ Answered by AbduraufKodiriy last updated on 10/Oct/20 $$\boldsymbol{{sinh}}\left(\boldsymbol{{x}}\right)=\frac{\boldsymbol{{e}}^{\boldsymbol{{x}}} −\boldsymbol{{e}}^{−\boldsymbol{{x}}}…
Question Number 117251 by mathmax by abdo last updated on 10/Oct/20 $$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)=\:\mathrm{ln}\left(\mathrm{3}−\mathrm{sin}\left(\mathrm{2x}\right)\right) \\ $$$$\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 116990 by Bird last updated on 08/Oct/20 $${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}^{{n}} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{cosA}\:{and}\:{chA} \\ $$$$\left.\mathrm{3}\right){determine}\:{sinA}\:{and}\:{shA} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com