Question Number 30549 by abdo imad last updated on 23/Feb/18 $${let}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{3}{n}} }{\left(\mathrm{3}{n}\right)!}\:\:{find}\:{S}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30547 by abdo imad last updated on 23/Feb/18 $${ind}\:{S}=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}^{\mathrm{3}} \:+{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}{{n}!}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30526 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{ax}}\:\:{with}\:{a}\in{C}\:\:\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{series}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30519 by abdo imad last updated on 22/Feb/18 $${let}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:\:{find}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} {C}_{{n}} ^{{k}} \left(\mathrm{1}+{j}\right)^{{k}} {j}^{\mathrm{2}{n}−\mathrm{2}{k}} \:. \\ $$ Answered by sma3l2996 last updated…
Question Number 30509 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:{continue}\:{at}\:{o}\:{and}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{f}\left(\mathrm{2}{x}\right)−{f}\left({x}\right)}{{x}}={l} \\ $$$${prove}\:{that}\:{f}\:{is}\:{derivable}\:{at}\:{o}\:{and}\:{f}^{'} \left(\mathrm{0}\right)={l}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30505 by abdo imad last updated on 22/Feb/18 $${find}\:\:{A}=\sum_{{k}=\mathrm{0}} ^{{n}} \:{ch}\left({a}+{kb}\right)\:{and}\:{B}=\sum_{{k}=\mathrm{0}} ^{{n}} \:{sh}\left({a}+{kb}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30495 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:\:\:\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30496 by abdo imad last updated on 22/Feb/18 $${find}\:\:{A}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}\left({kx}\right)\:{and}\:{B}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{sin}\left({kx}\right) \\ $$ Terms of…
Question Number 30492 by abdo imad last updated on 22/Feb/18 $${let}\:\left({u}_{\left.{n}\right)} \:\:\:/\:\:\:{u}_{{n}+\mathrm{1}} =\:{u}_{{n}} \:\:+\frac{\mathrm{1}}{{n}}\:\:\:{find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:{for}\right. \\ $$$${n}\rightarrow\infty\:. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 30490 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:{derivable}\:{at}\:{o}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{let} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} {f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:.{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} . \\ $$ Terms of Service Privacy…