Question Number 32287 by abdo imad last updated on 22/Mar/18 $$\left.\mathrm{1}\right)\:{for}\:{x}>\mathrm{0}\:{prove}\:{that}\:\frac{\mathrm{1}}{{x}+\mathrm{1}}\:\leqslant{ln}\left({x}+\mathrm{1}\right)−{lnx}\:\leqslant\:\frac{\mathrm{1}}{{x}} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{u}_{{n}} =\:\sum_{{p}=\mathrm{1}} ^{{kn}} \:\frac{\mathrm{1}}{{p}}\:\:\:{find}\:{lim}_{{n}\rightarrow\infty\:} \:{u}_{{n}} . \\ $$ Terms of Service Privacy Policy…
Question Number 32288 by abdo imad last updated on 22/Mar/18 $${study}\:{the}\:{function}\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{1}}\:{e}^{\frac{\mathrm{1}}{{x}}} \:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32284 by abdo imad last updated on 22/Mar/18 $${prove}\:{that}\:\forall\:{x}\in\left[\mathrm{0},\frac{\pi}{\mathrm{4}}\right]\:\:{x}\leqslant{tanx}\leqslant\mathrm{2}{x} \\ $$$$\left.\mathrm{2}\right)\:{find}\:\alpha_{{n}} \:{and}\:\beta_{{n}} \:{from}\:{R}\:/\:\:\alpha_{{n}} \leqslant\:\sum_{{k}=\mathrm{2}} ^{{n}} \:{tan}\left(\frac{\pi}{\mathrm{2}{n}}\right)\leqslant\:\beta_{{n}} \\ $$ Terms of Service Privacy Policy…
Question Number 32285 by abdo imad last updated on 22/Mar/18 $${let}\:{f}\left({x}\right)=\:{x}^{{n}−\mathrm{1}} {ln}\left(\mathrm{1}+{x}\right)\:{with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({p}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$ Terms of Service Privacy Policy…
Question Number 32282 by abdo imad last updated on 22/Mar/18 $${let}\:{give}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\:\:\:{find}\:\:{f}^{\left({n}\right)} \left({o}\right)\:.\: \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32283 by abdo imad last updated on 22/Mar/18 $${let}\:{give}\:{f}\left({x}\right)={x}+\mathrm{2}\:−\sqrt{{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{f}^{−\mathrm{1}} \left({x}\right)\:{inverse}\:{of}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\left({f}^{−\mathrm{1}} \right)^{'} \left({x}\right)\:. \\ $$ Commented by abdo imad last…
Question Number 32280 by abdo imad last updated on 22/Mar/18 $${let}\:{u}_{{n}} =\:{e}^{\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\mathrm{1}}} \:\:−\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:{and}\:{lim}_{{n}\rightarrow\infty} {u}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{study}\:{the}\:{convergence}\:{of}\:\:\Sigma{u}_{{n}} \:. \\ $$ Terms of…
Question Number 32276 by abdo imad last updated on 22/Mar/18 $${prove}\:{that}\:\sum_{{i}=\mathrm{1}} ^{{n}} \:\left(\prod_{{j}=\mathrm{0}} ^{{p}} \left({i}+{j}\right)\right)=\frac{{n}\left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)…\left({n}+{p}+\mathrm{1}\right)}{{p}+\mathrm{2}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32277 by abdo imad last updated on 22/Mar/18 $${for}\:{x}_{{i}} \:\in\left[\mathrm{0},\mathrm{1}\right]\:{prove}\:{that} \\ $$$$\left(\mathrm{1}−{x}_{\mathrm{1}} \right)\left(\mathrm{1}−{x}_{\mathrm{2}} \right)….\left(\mathrm{1}−{x}_{{n}} \right)\:\geqslant\mathrm{1}−\left({x}_{\mathrm{1}} +{x}_{\mathrm{2}} \:+….\:+{x}_{{n}} \right). \\ $$ Terms of Service…
Question Number 32274 by abdo imad last updated on 22/Mar/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\:\:\frac{\mathrm{2}^{{k}} }{{x}^{\mathrm{2}^{{k}} } \:+\mathrm{1}}\:=\:\frac{\mathrm{1}}{{x}−\mathrm{1}}\:−\:\frac{\mathrm{2}^{{n}+\mathrm{1}} }{{x}^{\mathrm{2}^{{n}+\mathrm{1}} \:} −\mathrm{1}}\:\:. \\ $$ Terms of Service Privacy…