Category: None

Question Number 154359 by ZiYangLee last updated on 17/Sep/21 $$\mathrm{If}\:{f}\left(\mathrm{0}\right)=\mathrm{1},\:{f}\left(\mathrm{2}\right)=\mathrm{3},\:{f}\:'\left(\mathrm{2}\right)=\mathrm{5}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\int_{\mathrm{0}} ^{\:\mathrm{1}} {x}\:{f}''\left(\mathrm{2}{x}\right)\:{dx}. \\ $$ Answered by aleks041103 last updated on 17/Sep/21 $$\int{xf}''\left(\mathrm{2}{x}\right){dx}=\int{xd}\left(\frac{\mathrm{1}}{\mathrm{2}}{f}'\left(\mathrm{2}{x}\right)\right)= \\…

Question Number 154337 by SANOGO last updated on 17/Sep/21 $${etudier}\:{la}\:{continuite},\:{et}\:{derivabilite}: \\ $$$${x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right)\:{si}\neq\mathrm{0}\:{et}\:{f}\left(\mathrm{0}\right)=\mathrm{0} \\ $$ Answered by puissant last updated on 17/Sep/21 $${posons}:\begin{cases}{{f}\left(\mathrm{0}\right)=\mathrm{0}\:{si}\:{x}=\mathrm{0}\:}\\{{f}\left({x}\right)={x}^{\mathrm{2}} {sin}\left(\frac{\mathrm{1}}{{x}}\right)\:,\:{sinon}..}\end{cases} \\…

Question Number 154301 by joki last updated on 16/Sep/21 $$\mathrm{of}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}\:\mathrm{to}\:\mathrm{400}\:\left(\mathrm{including}\:\mathrm{101}\:\mathrm{and}\:\mathrm{400}\:\right. \\ $$$$\left.\mathrm{themselves}\right)\:\mathrm{how}\:\mathrm{many}\:\mathrm{are}\:\mathrm{not}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{or}\:\mathrm{5}? \\ $$ Answered by mr W last updated on 16/Sep/21 $$\mathrm{400}−\mathrm{100}=\mathrm{300}\:{numbers} \\ $$$${divisible}\:{by}\:\mathrm{3}:\:\lfloor\frac{\mathrm{400}}{\mathrm{3}}\rfloor−\lfloor\frac{\mathrm{100}}{\mathrm{3}}\rfloor=\mathrm{100}…

Question Number 23223 by abwayh last updated on 27/Oct/17 Answered by mrW1 last updated on 27/Oct/17 $$\Rightarrow\frac{\mathrm{ln}\:\mathrm{a}}{\mathrm{ln}\:\mathrm{x}}+\frac{\mathrm{ln}\:\mathrm{a}}{\mathrm{ln}\:\mathrm{y}}=\mathrm{4}×\frac{\mathrm{ln}\:\mathrm{a}}{\mathrm{ln}\:\left(\mathrm{xy}\right)} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{ln}\:\mathrm{y}}=\frac{\mathrm{4}}{\mathrm{ln}\:\left(\mathrm{xy}\right)} \\ $$$$\Rightarrow\frac{\mathrm{ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}}{\left(\mathrm{ln}\:\mathrm{x}\right)\left(\mathrm{ln}\:\mathrm{y}\right)}=\frac{\mathrm{4}}{\mathrm{ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}} \\ $$$$\Rightarrow\left(\mathrm{ln}\:\mathrm{x}+\mathrm{ln}\:\mathrm{y}\right)^{\mathrm{2}} =\mathrm{4}\left(\mathrm{ln}\:\mathrm{x}\right)\left(\mathrm{ln}\:\mathrm{y}\right) \\…

Question Number 154291 by joki last updated on 16/Sep/21 $$\mathrm{Among}\:\mathrm{the}\:\mathrm{integers}\:\mathrm{101}−\mathrm{400},\mathrm{how}\:\mathrm{many}\:\mathrm{numbers} \\ $$$$\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{3}\:\mathrm{but}\:\mathrm{no}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}\:\mathrm{or}\:\mathrm{7} \\ $$ Answered by talminator2856791 last updated on 16/Sep/21 $$\: \\ $$$$\:\mathrm{102},\mathrm{105},…..,\mathrm{399} \\…