Question Number 2265 by B744237509 last updated on 12/Nov/15 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{3}{x}+{sin}\mathrm{2}{x}}{\mathrm{2}{x}+{sin}\mathrm{3}{x}}=? \\ $$$$ \\ $$$$ \\ $$ Answered by Filup last updated on 12/Nov/15 $$=\underset{{x}\rightarrow\mathrm{0}}…
Question Number 67799 by mathmax by abdo last updated on 31/Aug/19 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:−{e}^{{ia}} \right)\left({x}^{\mathrm{2}} −{e}^{{ib}} \right)}\:\:{with}\:{a}>\mathrm{0}\:{andb}>\mathrm{0} \\ $$ Commented by MJS last updated…
Question Number 133335 by Ahmed1hamouda last updated on 21/Feb/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 133334 by mnjuly1970 last updated on 21/Feb/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…\:{nice}\:\:\:\:\:\:{calculus}… \\ $$$$\:{prove}\:\:{that}:: \\ $$$$\:\:\:\boldsymbol{\phi}=\int_{−\infty} ^{\:+\infty} \frac{\:{cosh}\left({px}\right)}{{cosh}\left({x}\right)}\:=\:\frac{\pi}{{cos}\left(\frac{\pi{p}}{\mathrm{2}}\right)} \\ $$$$ \\ $$ Answered by mnjuly1970 last updated…
let-A-p-0-pi-x-p-cos-nx-dx-1-calculate-A-0-A-1-A-2-2-determine-a-relation-of-recurrence-between-A-p-
Question Number 67795 by mathmax by abdo last updated on 31/Aug/19 $${let}\:\:{A}_{{p}} =\int_{\mathrm{0}} ^{\pi} \:{x}^{{p}} \:{cos}\left({nx}\right){dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{\mathrm{0}} ,{A}_{\mathrm{1}} ,{A}_{\mathrm{2}} \\ $$$$\left.\mathrm{2}\right){determine}\:{a}\:{relation}\:{of}\:{recurrence}\:{between}\:\:{A}_{{p}} \\ $$ Commented…
Question Number 2258 by Filup last updated on 12/Nov/15 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sum}: \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{i}+\mathrm{1}} {ix}^{{i}} ={x}−\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{4}} +… \\ $$ Commented by Filup last…
Question Number 2253 by 123456 last updated on 11/Nov/15 $${f}_{{n}} :\left[\mathrm{0},\mathrm{1}\right]\rightarrow\left[\mathrm{0},\mathrm{1}\right],{g}:\left[\mathrm{0},\mathrm{1}\right]\rightarrow\left[\mathrm{0},\mathrm{1}\right] \\ $$$${f}_{{n}+\mathrm{1}} \left({x}\right)={g}\left[{f}_{{n}} \left({x}\right)\right]+{f}_{{n}} \left[{g}\left({x}\right)\right] \\ $$$${f}_{\mathrm{0}} \left({x}\right)={x} \\ $$$${f}_{\mathrm{4}} \left({x}\right)=? \\ $$$${g}\left({x}\right)={x}^{\mathrm{2}} ,{f}_{\mathrm{2}}…
Question Number 133321 by 777316 last updated on 21/Feb/21 $${Find}\:{x}\:: \\ $$$${sin}\left(\mathrm{3}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{2}{sin}\left({x}\right)\:=\:\sqrt{\mathrm{3}}{cos}\left({x}\right) \\ $$ Commented by bramlexs22 last updated on 21/Feb/21 $$\mathrm{x}=\frac{\mathrm{2}\pi}{\mathrm{3}} \\ $$$$\mathrm{sin}\:\left(\mathrm{3}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{sin}\:\left(\mathrm{2}×\frac{\mathrm{2}\pi}{\mathrm{3}}\right)−\mathrm{2sin}\:\left(\frac{\mathrm{2}\pi}{\mathrm{3}}\right)= \\…
Question Number 133320 by bramlexs22 last updated on 21/Feb/21 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\:\mathrm{n}^{\mathrm{2}} +\mathrm{2n}+\mathrm{4}\: \\ $$$$\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{7}\: \\ $$ Answered by EDWIN88 last updated on 21/Feb/21 $$\mathrm{let}\:\mathrm{n}\:=\:\mathrm{7k}+\mathrm{r}\:\mathrm{then}\:\mathrm{n}^{\mathrm{2}} +\mathrm{2n}+\mathrm{4}\:=\:\left(\mathrm{7k}+\mathrm{r}\right)^{\mathrm{2}} +\mathrm{2}\left(\mathrm{7k}+\mathrm{r}\right)+\mathrm{4}…
Question Number 2249 by Filup last updated on 11/Nov/15 $$\mathrm{With}\:\mathrm{linear}\:\mathrm{functions}\:{f}\left({x}\right)\:\mathrm{and}\:{g}\left({x}\right), \\ $$$$\mathrm{if}\:{f}\left({x}\right)\bot{g}\left({x}\right),\:\mathrm{then}: \\ $$$${m}_{{f}} {m}_{{g}} =−\mathrm{1}\:\:\:\:\mathrm{where}\:{m}_{{i}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{gradient} \\ $$$$\mathrm{of}\:\mathrm{function}\:{i}\left({x}\right). \\ $$$$ \\ $$$$\mathrm{Does}\:\mathrm{that}\:\mathrm{therefore}\:\mathrm{mean}\:\mathrm{that},\:\mathrm{if}\:\mathrm{given} \\ $$$$\mathrm{function}\:\left(\mathrm{including}\:\mathrm{non}−\mathrm{linear}\right)\:{f}\left({x}\right),…