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Author: Tinku Tara

If-f-x-x-x-x-find-d-dx-f-x-

Question Number 209924 by OmoloyeMichael last updated on 26/Jul/24 $$\boldsymbol{{If}}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\left(\boldsymbol{{x}}!\right)\centerdot\left(\boldsymbol{{x}}!!\right)\centerdot\left(\boldsymbol{{x}}!!!\right)\:\: \\ $$$$\boldsymbol{{find}}\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

lim-n-1-3n-1-1-3n-2-1-4n-

Question Number 209926 by depressiveshrek last updated on 26/Jul/24 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{1}}+\frac{\mathrm{1}}{\mathrm{3}{n}+\mathrm{2}}+…+\frac{\mathrm{1}}{\mathrm{4}{n}} \\ $$ Commented by Frix last updated on 26/Jul/24 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\:\frac{\mathrm{1}}{\mathrm{3}{n}+{k}}\:={H}_{\mathrm{4}{n}} −{H}_{\mathrm{3}{n}} \\…

Solve-sin-x-x-dx-

Question Number 209923 by OmoloyeMichael last updated on 26/Jul/24 $$\boldsymbol{{Solve}}:\:\int\frac{\boldsymbol{{sin}}\left(\boldsymbol{{x}}!\right)}{\boldsymbol{{x}}!}\boldsymbol{{dx}} \\ $$ Answered by MrGaster last updated on 03/Feb/25 $$\int\frac{\mathrm{sin}\left({x}!\right)}{{x}!}\mathrm{d}{x}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\int_{{k}\pi} ^{\left({k}+\mathrm{1}\right)} \frac{\mathrm{sin}\left({x}\right)!}{{x}!} \\…

Find-0-x-x-x-1-dx-x-fractional-part-x-full-part-

Question Number 209918 by hardmath last updated on 25/Jul/24 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\infty} \:\frac{\left\{\mathrm{x}\right\}^{\left[\boldsymbol{\mathrm{x}}\right]} }{\left[\mathrm{x}\right]\:+\:\mathrm{1}}\:\mathrm{dx}\:=\:? \\ $$$$\left\{\mathrm{x}\right\}\:\rightarrow\:\mathrm{fractional}\:\mathrm{part} \\ $$$$\left[\mathrm{x}\right]\:\:\:\rightarrow\:\mathrm{full}\:\mathrm{part} \\ $$ Answered by MM42 last updated on…