Question Number 155360 by mathlove last updated on 29/Sep/21 Answered by puissant last updated on 30/Sep/21 $$\psi\left(\frac{\mathrm{3}}{\mathrm{2}}\right)=\psi\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)=\psi\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\frac{\mathrm{1}}{\mathrm{2}}}=\psi\left(\frac{\mathrm{1}}{\mathrm{2}}\right)+\mathrm{2} \\ $$$${or}\:\psi\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=−\mathrm{2}{ln}\mathrm{2}−\gamma \\ $$$$\Rightarrow\:\psi\left(\frac{\mathrm{3}}{\mathrm{2}}\right)\:=\:−\mathrm{2}{ln}\mathrm{2}−\gamma+\mathrm{2}\:=\:\mathrm{2}+{ln}\frac{\mathrm{1}}{\mathrm{4}}−\gamma \\ $$ Terms of…
Question Number 155353 by zakirullah last updated on 29/Sep/21 $$\boldsymbol{{show}}\:\boldsymbol{{that}}\:\:\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{0}} \frac{\boldsymbol{{sinx}}}{\boldsymbol{{x}}}\:=\:\mathrm{1} \\ $$ Answered by puissant last updated on 29/Sep/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sinx}}{{x}}=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{sinx}−{sin}\mathrm{0}}{{x}−\mathrm{0}}={f}'\left(\mathrm{0}\right) \\ $$$${f}\left({x}\right)={sinx}\rightarrow{f}'\left({x}\right)={cosx}…
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Question Number 24260 by NECx last updated on 14/Nov/17 $${When}\:{a}\:{system}\:{of}\:{forces}\:{acts}\:{on} \\ $$$${a}\:{body}\:{moving}\:{in}\:{a}\:{circular}\:{path} \\ $$$${what}\:{happens}\:{to}\:{the}\:{resultant} \\ $$$${force}\:{when}: \\ $$$$\left.\mathrm{1}\right){there}'{s}\:{no}\:{friction} \\ $$$$\left.\mathrm{2}\right){there}'{s}\:{friction} \\ $$$$ \\ $$$$ \\…
Question Number 155331 by zakirullah last updated on 28/Sep/21 $$\mathrm{what}\:\mathrm{is}\:\mathrm{limit}?\:\mathrm{also}\:\mathrm{where}\:\mathrm{we}\:\mathrm{use}\:\mathrm{it}. \\ $$ Answered by TheHoneyCat last updated on 29/Sep/21 $$\mathrm{The}\:\mathrm{idea}\:\mathrm{of}\:{limit}\:\mathrm{is}\:\mathrm{very}\:\mathrm{very}\:\mathrm{general}. \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{present}\:\mathrm{in}\:\mathrm{post}\:\mathrm{fields}\:\mathrm{of}\:\mathrm{math} \\ $$$$\left(\mathrm{all}\:\mathrm{of}\:\mathrm{the}\:\mathrm{non}−\mathrm{descreet}\:\mathrm{ones},\:\mathrm{but}\:\mathrm{also}\:\mathrm{some}\:\mathrm{others}\right) \\…
Question Number 155316 by ZiYangLee last updated on 28/Sep/21 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}−{x}\right)=? \\ $$ Answered by puissant last updated on 28/Sep/21 $$=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{3}{x}}{\:{x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{3}{x}}}\:=\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{{x}}{{x}}×\frac{\mathrm{3}}{\mathrm{1}+\sqrt{\mathrm{1}+\frac{\mathrm{3}}{{x}}}}…
Question Number 155310 by SANOGO last updated on 28/Sep/21 $$\mathrm{lim}\:\:\:\:{U}_{{n}} =\underset{{k}={o}} {\overset{{n}−\mathrm{1}} {\sum}}\:\:\frac{{n}\left({ln}\left({n}+{k}\right)\right)−{ln}\left({n}\right)}{{n}^{\mathrm{2}} +{k}^{\mathrm{2}} } \\ $$ Answered by puissant last updated on 28/Sep/21 $$\underset{{x}\rightarrow\infty}…
Question Number 89755 by naka3546 last updated on 19/Apr/20 Commented by john santu last updated on 19/Apr/20 $$\mathrm{576}\:{cm}^{\mathrm{2}} \\ $$ Answered by $@ty@m123 last updated…
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Question Number 155265 by SANOGO last updated on 28/Sep/21 $${si}\:{E}\:{est}\:{la}\:{fonction}\:{partie}\:{entiere}\:,{et}\:{n}\:{un}\:{entier}\:{naturel} \\ $$$${alors}\:{I}=\int_{{o}} ^{{n}} {E}\left({x}\right)\:{vaut}? \\ $$ Answered by puissant last updated on 28/Sep/21 $${I}=\int_{\mathrm{0}} ^{{n}}…