Question Number 34677 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:\left[{x}\:+\frac{{k}}{{n}}\right]\:=\left[{nx}\right]\:\:\forall\:{n}\in\:\in{N}^{\bigstar} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34672 by math khazana by abdo last updated on 09/May/18 $${prove}\:{that}\:\forall{n}\in{N}\:\:\:\mid{sin}\left({nx}\right)\mid\leqslant{n}\mid{sinx}\mid\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34666 by math khazana by abdo last updated on 09/May/18 $${simplify}\:{sin}^{\mathrm{2}} \left(\:\frac{{arccosx}}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34664 by math khazana by abdo last updated on 09/May/18 $${simplify} \\ $$$${g}\left({x}\right)=\:{arctan}\left(\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\right)\:−{arctan}\left(\frac{{x}}{{x}+\mathrm{1}}\right)\:+{arctan}\left(\frac{{x}−\mathrm{1}}{{x}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34665 by math khazana by abdo last updated on 09/May/18 $${simplify}\:\:{sin}\:\left(\mathrm{2}{arcsinx}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34663 by math khazana by abdo last updated on 09/May/18 $${simplify}\: \\ $$$${f}\left({x}\right)={arcsin}\left(\sqrt{\left.\mathrm{1}−{x}^{\mathrm{2}} \right)}\:\:−{arctan}\left(\sqrt{\frac{\mathrm{1}−{x}}{\mathrm{1}+{x}}}\right)\right. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 34634 by abdo mathsup 649 cc last updated on 09/May/18 $${let}\:{f}\left({x}\right)={ln}\left(\mathrm{1}+{ix}\right)\:{with}\:\mid{x}\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{extract}\:{Re}\left({f}\left({x}\right)\right)\:{and}\:{Im}\left({f}\left({x}\right)\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{serie}. \\ $$ Commented by math khazana by abdo…
Question Number 34632 by math khazana by abdo last updated on 09/May/18 $${let}\:{z}\in{C}\:\:{developp}\:{at}\:{integrserie} \\ $$$${f}\left({z}\right)={ln}\left(\mathrm{1}+{z}\right)\:\:{with}\:\mid{z}\mid<\mathrm{1}\:. \\ $$$$\left.\mathrm{2}\right)\:{give}\:{ln}\left(\mathrm{2}+{i}\right)\:{at}\:{form}\:{of}\:{serie}. \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 100087 by mathmax by abdo last updated on 24/Jun/20 $$\mathrm{use}\:\mathrm{beta}\:\mathrm{function}\:\mathrm{to}\:\mathrm{calculate}\:\int_{\mathrm{0}} ^{\pi} \:\mathrm{sin}^{\mathrm{3}} \mathrm{x}\left(\mathrm{2}+\mathrm{cosx}\right)^{\mathrm{6}} \:\mathrm{dx} \\ $$ Commented by bemath last updated on 25/Jun/20…
Question Number 34485 by candre last updated on 07/May/18 $$\mathrm{is}\:\mathrm{there}\:\mathrm{a}\:\mathrm{function}\:\mathrm{such}\:\mathrm{that}: \\ $$$$\forall{x}\geqslant\mathrm{0};{f}\left({x}+{T}_{\mathrm{1}} \right)={f}\left({x}\right) \\ $$$$\forall{x}\leqslant\mathrm{0};{f}\left({x}−{T}_{\mathrm{2}} \right)={f}\left({x}\right) \\ $$$${f}\:\mathrm{is}\:\mathrm{diferentiabre}\:\mathrm{in}\:{x}=\mathrm{0} \\ $$ Answered by MJS last updated…