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
Question Number 97985 by abdomathmax last updated on 10/Jun/20 $$\mathrm{let}\:\mathrm{S}_{\mathrm{n}} =\sum_{\mathrm{k}=\mathrm{1}} ^{\mathrm{n}} \:\frac{\mathrm{1}}{\:\sqrt{\mathrm{n}^{\mathrm{2}} +\mathrm{2kn}}} \\ $$$$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\mathrm{S}_{\mathrm{n}} \\ $$ Answered by maths mind last updated…
Question Number 97981 by abdomathmax last updated on 10/Jun/20 $$\mathrm{calculate}\:\mathrm{lim}_{\mathrm{x}\rightarrow\mathrm{1}^{+} } \:\:\int_{\mathrm{x}−\mathrm{1}} ^{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \:\frac{\mathrm{dt}}{\mathrm{ln}\left(\mathrm{1}+\mathrm{t}\right)} \\ $$ Answered by mathmax by abdo last updated on…
Question Number 97979 by abdomathmax last updated on 10/Jun/20 $$\mathrm{find}\:\mathrm{lim}_{\mathrm{n}\rightarrow+\infty} \:\left(\mathrm{C}_{\mathrm{2n}} ^{\mathrm{n}} \right)^{\frac{\mathrm{1}}{\mathrm{n}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 163508 by alcohol last updated on 07/Jan/22 $${etudier}\:{la}\:{continuite}\:{de}\:\left[\:{x}\:\right]\:−\:\sqrt{{x}\:−\:\left[\:{x}\:\right]} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 32369 by prof Abdo imad last updated on 23/Mar/18 $${prove}\:{that}\:\:{n}^{−\alpha} \:\sim\:\int_{{n}} ^{{n}+\mathrm{1}} \:{t}^{−\alpha} {dt} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}^{\alpha} }\:\sim\:\:\frac{{n}^{\mathrm{1}−\alpha} }{\mathrm{1}−\alpha}\:{if}\:\:\alpha<\mathrm{1}\:{and} \\ $$$$\sum_{{k}=\mathrm{1}} ^{{n}}…