Question Number 132861 by Dwaipayan Shikari last updated on 17/Feb/21 $$\int_{\mathrm{0}} ^{\infty} \frac{{cos}\left({x}\pi{t}\right)}{{cosh}\left(\pi{x}\right)}{e}^{−\pi^{\mathrm{2}} {x}} {dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 67298 by Rio Michael last updated on 25/Aug/19 $${Find}\:\:{the}\:{third}\:{degree}\:{polynomial}\:{which}\:{vanishes}\:{when} \\ $$$${x}\:=−\mathrm{1}\:{and}\:{x}\:=\:\mathrm{2},\:{which}\:{has}\:{a}\:{value}\:\mathrm{8}\:{when}\:{x}\:=\mathrm{0}\:{and}\:{leaves}\:{a}\:{remainder}\:\frac{\mathrm{16}}{\mathrm{3}}\:{when} \\ $$$${divided}\:{by}\:\:\mathrm{3}{x}\:+\:\mathrm{2}. \\ $$ Commented by Prithwish sen last updated on 25/Aug/19…
Question Number 67299 by Rio Michael last updated on 25/Aug/19 $${G}\left({x}\right)=\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right){Q}\left({x}\right)\:+\:{px}\:+{q} \\ $$$$\left.{a}\right)\:{Given}\:{that}\:{G}\left({x}\right)\:{leaves}\:{a}\:{remainder}\:{of}\:\mathrm{8}\:{and}\:−\mathrm{24}\:{when}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\:{and}\: \\ $$$$\left({x}+\mathrm{3}\right)\:{respectively},{find}\:{the}\:{remainder}\:{when}\:{G}\left({x}\right)\:{is}\:{divided}\:{by}\:\left({x}+\mathrm{1}\right)\left({x}+\mathrm{3}\right). \\ $$$$\left.{b}\right)\:\:{Given}\:{that}\:{x}+\mathrm{2}\:{is}\:{a}\:{factor}\:{of}\:{G}\left({x}\right)\:{and}\:{that}\:{the}\:{graph}\:{of}\:{G}\left({x}\right)\:{passes}\:{through} \\ $$$${the}\:{point}\:{with}\:{coordinates}\:\left(\mathrm{0},\mathrm{6}\right)\:{find}\:{G}\left({x}\right) \\ $$ Commented by Rasheed.Sindhi last…
Question Number 132827 by victoras last updated on 16/Feb/21 Commented by mr W last updated on 16/Feb/21 $${impossible}! \\ $$ Commented by Dwaipayan Shikari last…
Question Number 132715 by Dwaipayan Shikari last updated on 16/Feb/21 $$\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{4}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{5}^{\mathrm{3}} }+\frac{\mathrm{1}}{\mathrm{7}^{\mathrm{3}} }−\frac{\mathrm{1}}{\mathrm{8}^{\mathrm{3}} }+… \\ $$ Answered by Olaf last updated on…
Question Number 67148 by Cmr 237 last updated on 29/Aug/19 $$\mathrm{explicitez}\:\:\:\mathrm{la}\:\mathrm{suite}\:\mathrm{u}_{\mathrm{n}} \mathrm{definie}\:\mathrm{par}\:\mathrm{la}\:\mathrm{relation}; \\ $$$$\begin{cases}{\mathrm{u}_{\mathrm{0}} =\mathrm{0},\:\mathrm{u}_{\mathrm{1}} =\mathrm{1}}\\{\mathrm{u}_{\mathrm{n}+\mathrm{2}} =\mathrm{u}_{\mathrm{n}+\mathrm{1}} +\mathrm{u}_{\mathrm{n}} \:\:\:\forall\mathrm{n}\in\nmid\boldsymbol{\mathrm{N}}}\end{cases} \\ $$$$\boldsymbol{{u}}_{\boldsymbol{{n}}} =???????? \\ $$$$−\mathrm{calculer}\:\mathrm{la}\:\mathrm{lim}\underset{\mathrm{n}\rightarrow\infty} {\:}\frac{\mathrm{u}_{\mathrm{n}+\mathrm{1}}…
Question Number 1594 by 123456 last updated on 24/Aug/15 $${f}\left({x}\right)=\underset{\mathrm{0}} {\overset{{x}} {\int}}{t}^{{x}} {dt},{x}>−\mathrm{1} \\ $$$$\underset{{x}\rightarrow−\mathrm{1}^{+} } {\mathrm{lim}}{f}\left({x}\right)=? \\ $$$${f}\left({x}+\mathrm{1}\right)−{f}\left({x}\right)=? \\ $$ Commented by 112358 last…
Question Number 1573 by 123456 last updated on 20/Aug/15 $$\underset{\epsilon\rightarrow+\infty} {\mathrm{lim}}\:\underset{\mathrm{0}} {\overset{\epsilon} {\int}}\epsilon^{−{t}} {dt}=? \\ $$ Commented by 112358 last updated on 21/Aug/15 $${Let}\:{I}\left(\epsilon\right)=\int_{\mathrm{0}} ^{\:\epsilon}…
Question Number 1559 by 123456 last updated on 19/Aug/15 $$\mathrm{find}\:\mathrm{complex}\:\mathrm{number}\:\alpha,\beta\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha^{{n}} =\beta^{{m}} \\ $$$$\beta^{{u}} =\alpha^{{v}} \\ $$$${n},{m},{u},{v}\in\mathbb{Z} \\ $$$$\boldsymbol{{Q}}\mathrm{1498} \\ $$ Answered by Rasheed…
Question Number 1557 by 123456 last updated on 19/Aug/15 $$\mathrm{find}\:\alpha,\beta,\gamma\:\mathrm{such}\:\mathrm{that} \\ $$$$\alpha=\beta^{\mathrm{2}} \\ $$$$\beta^{\mathrm{3}} =\gamma^{\mathrm{4}} \\ $$$$\gamma^{\mathrm{5}} =\alpha^{\mathrm{6}} \\ $$ Commented by 123456 last updated…