Question Number 207648 by SANOGO last updated on 22/May/24 $${f}_{{n}} \left({x}\right)=\frac{{n}}{\mathrm{1}+{x}^{\mathrm{2}} }{sin}\left(\frac{{x}}{{n}}\right)\:\:/{x}\in\left[\mathrm{0},\mathrm{1}\right]\:,\:\:{n}\geqslant\mathrm{1} \\ $$$${calculer}\:{lim}\:{n}\rightarrow\infty\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx} \\ $$ Commented by mr W last updated…
Question Number 207665 by efronzo1 last updated on 22/May/24 $$\:\:\:\:\frac{\mathrm{1}}{\mathrm{1}}\begin{pmatrix}{\mathrm{20}}\\{\:\:\mathrm{0}}\end{pmatrix}\:+\frac{\mathrm{1}}{\mathrm{2}}\begin{pmatrix}{\mathrm{20}}\\{\:\:\mathrm{1}}\end{pmatrix}\:+\frac{\mathrm{1}}{\mathrm{3}}\begin{pmatrix}{\mathrm{20}}\\{\:\:\mathrm{2}}\end{pmatrix}\:+…+\frac{\mathrm{1}}{\mathrm{21}}\:\begin{pmatrix}{\mathrm{20}}\\{\mathrm{20}}\end{pmatrix}\:=? \\ $$ Answered by Tinku Tara last updated on 22/May/24 $$\left(\mathrm{1}+{x}\right)^{\mathrm{20}} =\underset{{n}=\mathrm{0}} {\overset{\mathrm{20}} {\sum}}\begin{pmatrix}{\mathrm{20}}\\{{n}}\end{pmatrix}{x}^{{n}} \\…
Question Number 207683 by efronzo1 last updated on 22/May/24 Answered by mr W last updated on 23/May/24 Commented by mr W last updated on 22/May/24…
Question Number 207641 by hardmath last updated on 21/May/24 $$\mathrm{Find}:\:\:\:\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:\mathrm{40}\:−\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{20}}\:\:=\:\:? \\ $$ Commented by Frix last updated on 22/May/24 $$\mathrm{4}−\mathrm{2}\sqrt{\mathrm{7}}\mathrm{cos}\:\frac{\pi+\mathrm{2sin}^{−\mathrm{1}} \:\frac{\mathrm{37}\sqrt{\mathrm{7}}}{\mathrm{98}}}{\mathrm{6}} \\ $$ Answered…
Question Number 207620 by Ghisom last updated on 21/May/24 $$\mathrm{prove}\:\mathrm{that}\:\underset{−{a}} {\overset{{a}} {\int}}\:\frac{{dx}}{{x}^{{n}} +\mathrm{1}+\sqrt{{x}^{\mathrm{2}{n}} +\mathrm{1}}}={a} \\ $$ Answered by Berbere last updated on 21/May/24 $$\int_{−{a}} ^{{a}}…
Question Number 207638 by hardmath last updated on 21/May/24 Commented by TonyCWX08 last updated on 22/May/24 $${arcsin}\left({sin}\mathrm{5}\right)=\mathrm{5} \\ $$$${arccis}\left({cos}\mathrm{6}\right)=\mathrm{6} \\ $$$${arctan}\left({tan}\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{5}+\mathrm{6}+\mathrm{2}=\mathrm{13} \\ $$…
Question Number 207639 by hardmath last updated on 21/May/24 Commented by Berbere last updated on 21/May/24 $${false}\:{not}\:{true}\: \\ $$$$\begin{pmatrix}{\mathrm{2}{n}}\\{{n}}\end{pmatrix}\sim\frac{\mathrm{4}^{{n}} }{\:\sqrt{\pi{n}}} \\ $$$$\frac{\mathrm{2}^{−\mathrm{2}\left({n}−\mathrm{1}\right)} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{3}\right)}{\left({n}+\mathrm{2}\right)\left({n}+\mathrm{4}\right)}\begin{pmatrix}{{n}}\\{\mathrm{2}{n}}\end{pmatrix}^{\mathrm{2}} \sim\frac{\mathrm{4}^{{n}} }{\pi{n}}\:{diverge}…
Question Number 207634 by SANOGO last updated on 21/May/24 $${calculer}\:{lim}\:\:{n}\rightarrow+{oo}\:{f}_{{n}} \left({x}\right) \\ $$$${f}_{{n}} \left({x}\right)=\int_{\mathrm{0}^{} } ^{+{oo}} \frac{{ne}^{−{x}} }{\mathrm{1}+{nx}}{dx}\:\:\:/{x}\in\left[\mathrm{0}+{oo}\left[\right.\right. \\ $$ Answered by Berbere last updated…
Question Number 207615 by mr W last updated on 21/May/24 $$\begin{cases}{{u}_{{n}+\mathrm{1}} =\frac{{au}_{{n}} +{b}}{{cu}_{{n}} +{d}}}\\{{u}_{\mathrm{0}} ={k}}\end{cases} \\ $$$${find}\:{u}_{{n}} \:{in}\:{terms}\:{of}\:{n}. \\ $$ Commented by mr W last…
Question Number 207610 by Davidtim last updated on 20/May/24 $${we}\:{have}\:\mathrm{100}\:{money}\:{if}\:{we}\:{want}\:{to}\:{buy}\:\mathrm{100}\:{Donkys}\:{Horses} \\ $$$${and}\:{Camels}\:{mixed}\:{while}\:\mathrm{20}\:{Donkys} \\ $$$${cost}\:\mathrm{1}\:{money},\:\mathrm{1}\:{Horse}\:{costs}\:\mathrm{1}\:{money}\:{and} \\ $$$$\mathrm{1}\:{Camel}\:{costs}\:\mathrm{5}\:{money}. \\ $$$${find}\:{total}\:{number}\:{of}\:{Donkys},\:{Horses}, \\ $$$${and}\:{Camels}. \\ $$ Commented by Davidtim…