Question Number 75105 by chess1 last updated on 07/Dec/19 Commented by MJS last updated on 07/Dec/19 $$\mathrm{arctan}\:\frac{\mathrm{40}−\mathrm{4}\sqrt{\mathrm{2}}}{\mathrm{21}} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 140637 by Mathspace last updated on 10/May/21 $${let}\:{f}\left({x}\right)={x}^{\mathrm{2}{n}} \:{e}^{−\mathrm{3}{x}} \\ $$$${find}\:\:{f}^{\left({n}\right)} \left({o}\right)\:{and} \\ $$$${calculate}\:{f}^{\left(\mathrm{2021}\right)} \left(\mathrm{0}\right) \\ $$ Answered by mathmax by abdo last…
Question Number 75102 by Rio Michael last updated on 07/Dec/19 $$\mathrm{show}\:\mathrm{by}\:\mathrm{integration}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{semi}−\mathrm{circular}\:\mathrm{lamina}\:\mathrm{of}\:\mathrm{radius}\:{a}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{is}\:\:\:\frac{\mathrm{4}{a}}{\mathrm{3}\pi}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 140636 by Mathspace last updated on 10/May/21 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on 10/May/21…
Question Number 140639 by Mathspace last updated on 10/May/21 $${let}\:{U}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{x}^{{n}} {logx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{explicite}\:{U}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{fond}\:{nature}\:{of}\:\Sigma\:{U}_{{n}} \\ $$$$\left({n}\:{integr}\:{natural}\right) \\ $$ Answered…
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Question Number 75100 by Rio Michael last updated on 07/Dec/19 $$\:{find}\:{the}\:{intervals}\:{cor}\:{which}\:{the}\:{function} \\ $$$${h}\left({x}\right)\:=\:{x}^{\mathrm{3}} −\mathrm{3}{x}\:{is} \\ $$$$\left.{a}\right)\:{strickly}\:{increasing} \\ $$$$\left.{b}\right)\:{strickly}\:{decreasing} \\ $$$$ \\ $$ Answered by mr…
Question Number 140638 by Mathspace last updated on 10/May/21 $${let}\:{f}\left({x}\right)={arctan}\left(\frac{\mathrm{2}}{{x}}\right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Answered by Dwaipayan Shikari last updated on 10/May/21 $${f}\left({x}\right)={f}\left(\mathrm{0}\right)+\frac{{f}'\left(\mathrm{0}\right)}{\mathrm{1}!}{x}+\frac{{f}''\left(\mathrm{0}\right)}{\mathrm{2}!}{x}^{\mathrm{2}} +.. \\…
Question Number 75101 by Rio Michael last updated on 07/Dec/19 $${the}\:{vector}\:{equations}\:{of}\:{two}\:{lines}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} \:{is}\:{given}\:{by} \\ $$$$\:{L}_{\mathrm{1}} :{r}=\:\boldsymbol{{i}}−\boldsymbol{{j}}+\mathrm{3}\boldsymbol{{k}}\:+\:\lambda\left(\boldsymbol{{i}}−\boldsymbol{{j}}\:+\boldsymbol{{k}}\right) \\ $$$${L}_{\mathrm{2}} \::\:{r}=\:\mathrm{2}\boldsymbol{{i}}+{a}\boldsymbol{{j}}\:+\:\mathrm{6}\boldsymbol{{k}}\:+\:\mu\left(\mathrm{2}\boldsymbol{{i}}\:+\:\boldsymbol{{j}}\:+\:\mathrm{3}\boldsymbol{{k}}\right) \\ $$$${where}\:{a},\lambda,\mu\:{are}\:{real}\:{constants}. \\ $$$${given}\:{that}\:{L}_{\mathrm{1}} \:{and}\:{L}_{\mathrm{2}} \:{intersect}\:{find}…
Question Number 75098 by Rio Michael last updated on 07/Dec/19 $$\mathrm{the}\:\mathrm{function}\:\mathrm{f}\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}\:{f}\left({x}\right)\:=\:\frac{\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{1}} \\ $$$$\left.{a}\right)\:\mathrm{Express}\:\mathrm{f}\:\mathrm{into}\:\mathrm{partial}\:\mathrm{fraction} \\ $$$$\mathrm{b}.\mathrm{show}\:\mathrm{that}\:\int_{\mathrm{3}} ^{\mathrm{5}} {f}\left({x}\right)\:{dx}\:=\:{ln}\left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$ Answered by peter frank last…
Question Number 75099 by Rio Michael last updated on 07/Dec/19 $${Given}\:{the}\:{matrix}\: \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{2}}&{\:−\mathrm{1}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{0}}\end{pmatrix}\:\:{and}\:{B}=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{2}}&{−\mathrm{2}}&{\mathrm{1}}\\{−\mathrm{4}}&{−\mathrm{5}}&{\mathrm{2}}\end{pmatrix} \\ $$$${find}\:{the}\:{matrix}\:{product}\:{AB}\:{and}\:{BA} \\ $$$${state}\:{the}\:{relationship}\:{between}\:{A}\:{and}\:{B} \\ $$$${find}\:{also}\:{the}\:{matrix}\:{product}\:{BM},\:{where}\:{M}=\begin{pmatrix}{\mathrm{8}}\\{−\mathrm{7}}\\{\mathrm{1}}\end{pmatrix} \\ $$$${Hence}\:{solve}\:{the}\:{system}\:{of}\:{equations}: \\ $$$$\:\:{x}−{y}\:+\:{z}\:=\:\mathrm{8}, \\ $$$$\:\:\:\:\:\:\:\mathrm{2}{y}\:−{z}\:=−\mathrm{7},…