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}}} \\ $$ Answered by maths mind last updated on 11/Jun/20…
Question Number 97988 by abdomathmax last updated on 10/Jun/20 $$\mathrm{calculate}\:\mathrm{by}\:\mathrm{recurrence}\:\mathrm{A}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{cos}^{\mathrm{n}} \mathrm{x}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 97984 by abdomathmax last updated on 10/Jun/20 $$\mathrm{calculate}\:\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{n}} \:\frac{\left(−\mathrm{1}\right)^{\mathrm{k}} }{\mathrm{2k}+\mathrm{1}}\:\mathrm{C}_{\mathrm{n}} ^{\mathrm{k}} \\ $$ Answered by mr W last updated on 11/Jun/20 $$\left(\mathrm{1}−{x}^{\mathrm{2}}…
Question Number 97983 by abdomathmax last updated on 10/Jun/20 $$\mathrm{f}\:\mathrm{continue}\:\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right]\:\mathrm{and}\:\mathrm{f}\left(\mathrm{x}\right)>\mathrm{0}\:\mathrm{on}\:\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{prove}\:\mathrm{that}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{lnf}\left(\mathrm{x}\right)\mathrm{dx}\leqslant\mathrm{ln}\left(\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com