Question Number 98180 by abdomathmax last updated on 12/Jun/20 $$\mathrm{solve}\:\:\mathrm{xy}^{''} \:+\left(\mathrm{x}^{\mathrm{3}} +\mathrm{1}\right)\mathrm{y}\:=\mathrm{3e}^{\mathrm{2x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98178 by abdomathmax last updated on 12/Jun/20 $$\mathrm{calculate}\:\:\sum_{\mathrm{p}=\mathrm{0}} ^{\mathrm{n}} \:\left(\mathrm{z}+\mathrm{1}\right)^{\mathrm{p}} \\ $$$$\mathrm{with}\:\mathrm{z}\:\mathrm{root}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}=\mathrm{0} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 98118 by abdomathmax last updated on 11/Jun/20 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\left(\xi\left(\mathrm{2n}\right)−\mathrm{1}\right)\mathrm{x}^{\mathrm{2n}} \\ $$$$\xi\left(\mathrm{x}\right)=\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{x}} } \\ $$ Answered by maths mind last updated…
Question Number 32490 by NECx last updated on 26/Mar/18 $${if}\:{f}\left({x}\right)=\mid{x}\mid\:{and}\:{g}\left({x}\right)=\mathrm{2}{x}−\mathrm{3}.{Find} \\ $$$${the}\:{domain}\:{of}\:{gof} \\ $$ Answered by MJS last updated on 26/Mar/18 $${g}\circ{f}={g}\left({f}\left({x}\right)\right)=\mathrm{2}\mid{x}\mid−\mathrm{3} \\ $$$$\mathrm{domain}:\:{x}\in\mathbb{R} \\…
Question Number 32489 by NECx last updated on 26/Mar/18 $${find}\:{the}\:{range}\:{of}\:{f}\left({x}\right)=\mathrm{1}+\sqrt{\mathrm{2}{x}−\mathrm{1}} \\ $$ Commented by prof Abdo imad last updated on 28/Mar/18 $${D}_{{f}} =\left[\frac{\mathrm{1}}{\mathrm{2}},+\infty\left[\:\:{and}\:{f}^{'} \left({x}\right)\:=\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}{x}−\mathrm{1}}}\:\:>\mathrm{0}\:{on}\right]\frac{\mathrm{1}}{\mathrm{2}},+\infty\left[\right.\right. \\…
Question Number 32486 by abdo imad last updated on 25/Mar/18 $${find}\:{lim}_{{n}\rightarrow\infty} \:\:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:{sin}\left(\frac{\mathrm{1}}{{k}}\right). \\ $$ Commented by abdo imad last updated on 26/Mar/18 $${let}\:{put}\:{S}_{{n}}…
Question Number 32487 by abdo imad last updated on 25/Mar/18 $${let}\:{x}>\mathrm{1}\:{and}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{{x}} }\:\left({zeta}\:{function}\:{of}\:{Rieman}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow+\infty} \xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right){let}\:{consider}\:\:{s}\left({x}\right)=\sum_{{n}=\mathrm{2}} ^{\infty} \:\:\frac{\xi\left({n}\right)}{{n}}\:{x}^{{n}} \:{study}\:{the}\:{convergence} \\ $$$${of}\:{s}\left({x}\right)\:{and}\:{find}\:{a}\:{simple}\:{form}\:{of}\:{s}\left({x}\right). \\…
Question Number 32485 by abdo imad last updated on 25/Mar/18 $${let}\:{give}\:\alpha>\mathrm{1}\:{find}\:{lim}_{{n}\rightarrow\infty} \:\:\sum_{{k}={n}+\mathrm{1}} ^{\mathrm{2}{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:. \\ $$ Commented by abdo imad last updated on 28/Mar/18…
Question Number 97990 by abdomathmax last updated on 10/Jun/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}} ^{\mathrm{x}^{\mathrm{2}} } \:\:\frac{\mathrm{lnt}}{\left(\mathrm{t}−\mathrm{1}\right)^{\mathrm{2}} }\mathrm{dt} \\ $$ Answered by maths mind last updated on…
Question Number 97987 by abdomathmax last updated on 10/Jun/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \sqrt{\frac{\mathrm{n}−\mathrm{k}}{\mathrm{n}^{\mathrm{3}} −\mathrm{n}^{\mathrm{2}} \mathrm{k}}} \\ $$ Answered by maths mind last updated on 11/Jun/20…