Question Number 46060 by samitoh last updated on 20/Oct/18 $${determine}\:{whether}\:{or}\:{not}\:\:\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left[\:\:\:\:\:\right. \\ $$$${is}\:{continuous} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 20/Oct/18 $${a}\:{function}\:{f}\left({x}\right)\:{will}\:{be}\:{continuous}\:{at}\:{x}={a} \\ $$$${when}\:\underset{{x}\rightarrow{a}−}…
Question Number 111535 by Aina Samuel Temidayo last updated on 04/Sep/20 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}^{\mathrm{2}} −\mathrm{c}\:\mathrm{satisfy}\:−\mathrm{4}\leqslant\mathrm{f}\left(\mathrm{1}\right)\leqslant−\mathrm{1} \\ $$$$\mathrm{and}\:−\mathrm{1}\leqslant\mathrm{f}\left(\mathrm{2}\right)\leqslant\mathrm{5},\:\mathrm{then} \\ $$$$ \\ $$$$\mathrm{A}.\:\mathrm{7}\leqslant\mathrm{f}\left(\mathrm{3}\right)\leqslant\mathrm{26}\:\mathrm{B}.\:−\mathrm{1}\leqslant\mathrm{f}\left(\mathrm{3}\right)\leqslant\mathrm{20}\:\mathrm{C}. \\ $$$$−\mathrm{4}\leqslant\mathrm{f}\left(\mathrm{3}\right)\leqslant\mathrm{15}\:\mathrm{D}.\:\frac{−\mathrm{28}}{\mathrm{3}}\leqslant\mathrm{f}\left(\mathrm{3}\right)\leqslant\frac{\mathrm{35}}{\mathrm{3}}\:\mathrm{E}. \\ $$$$\frac{\mathrm{8}}{\mathrm{3}}\leqslant\mathrm{f}\left(\mathrm{3}\right)\leqslant\frac{\mathrm{13}}{\mathrm{3}} \\ $$…
Question Number 111520 by mathmax by abdo last updated on 04/Sep/20 $$\mathrm{find}\:\mathrm{nature}\:\mathrm{of}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{n}^{\mathrm{p}} }{\mathrm{n}!}\:\:\:\left(\mathrm{p}\:\mathrm{natural}\:\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 45968 by maxmathsup by imad last updated on 19/Oct/18 $$\left.\mathrm{1}\right){find}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{cos}\left({nx}\right)}{{n}}\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{{sin}\left({nx}\right)}{{n}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{cos}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{3}}\right)\:{and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}}{sin}\left(\frac{\mathrm{2}{n}\pi}{\mathrm{3}}\right) \\ $$ Commented…
Question Number 45963 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}}{\left(\mathrm{4}{n}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}} }\:. \\ $$ Commented by maxmathsup by imad last updated…
Question Number 45961 by maxmathsup by imad last updated on 19/Oct/18 $${let}\:{f}_{{n}} \left({x}\right)=\left(−\mathrm{1}\right)^{{n}} \:{ln}\left(\mathrm{1}+\frac{{x}^{\mathrm{2}} }{{n}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}\right)\:{and}\:{f}\left({x}\right)=\Sigma\:{f}_{{n}} \left({x}\right) \\ $$$${find}\:{lim}_{{x}\rightarrow+\infty} {f}\left({x}\right). \\ $$ Terms of Service…
Question Number 45962 by maxmathsup by imad last updated on 19/Oct/18 $${study}\:{the}\:{convervence}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}}{{nln}\left({n}+\mathrm{1}\right)} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 45960 by maxmathsup by imad last updated on 19/Oct/18 $${find}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{x}^{{n}} {sin}\left({nx}\right)}{{n}} \\ $$ Answered by Smail last updated on 22/Oct/18 $${f}\left({x}\right)={Im}\left(\underset{{n}=\mathrm{1}}…
Question Number 45957 by maxmathsup by imad last updated on 19/Oct/18 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}!\left({n}−{k}\right)!}\:\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} {u}_{{n}} \\ $$ Commented by maxmathsup by imad last…
Question Number 45792 by maxmathsup by imad last updated on 16/Oct/18 $${let}\:{u}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{\left[{k}\right]} }{{k}}\:\:{and}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$$$\left.\mathrm{1}\right){calculate}\:{u}_{{n}} \:{interms}\:{of}\:{H}_{{n}} \\ $$$$\left.\mathrm{2}\right){study}\:{the}\:{convergence}\:{of}\:\left({u}_{{n}} \right)…