Question Number 183690 by paul2222 last updated on 28/Dec/22 Answered by mr W last updated on 29/Dec/22 $${T}_{{n}} =\frac{{n}}{{a}_{{n}} } \\ $$$${a}_{{n}} =\mathrm{1}^{\mathrm{6}} +\mathrm{2}^{\mathrm{6}} +\mathrm{3}^{\mathrm{6}}…
Question Number 52610 by Kunal12588 last updated on 10/Jan/19 $$\:{please}\:{help}\:{me} \\ $$$${y}=\sqrt{\mathrm{9}−{x}^{\mathrm{2}} } \\ $$$${Q}\:{find}\:{domain}\:{and}\:{range}\:{of}\:{given}\:{real}\:{function} \\ $$$${i}\:{found}\:{the}\:{domain}=\left[−\mathrm{3},\mathrm{3}\right] \\ $$$${but}\:{for}\:{range}\:{i}\:{followed}\:{this}\:{way} \\ $$$${y}^{\mathrm{2}} =\mathrm{9}−{x}^{\mathrm{2}} \\ $$$${x}^{\mathrm{2}} =\mathrm{9}−{y}^{\mathrm{2}}…
Question Number 118118 by naka3546 last updated on 15/Oct/20 $${f}\left({x}+{y}\right)\:=\:{f}\left({x}\right)\:{f}\left({y}\right)\:\:\:\forall{x}\:\in\:\mathbb{R} \\ $$$${f}\left(\mathrm{1}\right)\:=\:\mathrm{8} \\ $$$${f}\left(\frac{\mathrm{2}}{\mathrm{3}}\right)\:=\:? \\ $$ Answered by mr W last updated on 15/Oct/20 $${f}\left({x}\right)={a}^{{x}}…
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Question Number 52542 by hassentimol last updated on 09/Jan/19 $$\mathrm{Let}\:{f}\left({x}\right)\:=\:\frac{\:\mathrm{5}{x}\:+\:\mathrm{40}\:}{{x}\:+\:\mathrm{2}} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:{f}\left(\mathrm{4}\right)\:\mathrm{without} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\mathrm{question}\:\left(\mathrm{2}\right), \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:{f}\left({x}\right), \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Calculate}\:\:\underset{{x}\:\rightarrow\:+\infty} {\mathrm{lim}}\:{f}\left({x}\right)\:. \\ $$$$\mathrm{All}\:\mathrm{your}\:\mathrm{answers}\:\mathrm{should}\:\mathrm{be}\:\mathrm{correctly}\:\mathrm{proved}\:\mathrm{and}\:\mathrm{detailed}. \\ $$$$ \\ $$$${Can}\:{you}\:{please}\:{help}\:{me}\:{for}\:{that}\:{exercise}.…
Question Number 118043 by prakash jain last updated on 14/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{the}\:\mathrm{range} \\ $$$$\left[\mathrm{1},\mathrm{10}^{{n}} −\mathrm{1}\right]\:\mathrm{are}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{9}? \\ $$$$\mathrm{digit}\:\mathrm{repetitions}\:\mathrm{are}\:\mathrm{not}\:\mathrm{allowed}. \\ $$ Commented by mr W last updated on…
Question Number 52498 by Joel578 last updated on 09/Jan/19 $$\mathrm{Let}\:{z}\:\mathrm{is}\:\mathrm{complex}\:\mathrm{number}\:\mathrm{and}\:\mathrm{satisfy}\:{z}^{\mathrm{2017}} \:=\:\mathrm{1},\:\:{z}\:\neq\:\mathrm{1} \\ $$$$\mathrm{Find}\:\left(\mathrm{1}\:+\:{z}\right)\left(\mathrm{1}\:+\:{z}^{\mathrm{2}} \right)\left(\mathrm{1}\:+\:{z}^{\mathrm{3}} \right)\ldots\left(\mathrm{1}\:+\:{z}^{\mathrm{2016}} \right) \\ $$ Commented by mr W last updated on…
Question Number 52490 by Gulay last updated on 08/Jan/19 Commented by Gulay last updated on 08/Jan/19 $$\mathrm{sir}\:\mathrm{could}\:\mathrm{you}\:\mathrm{he}\:\mathrm{me}? \\ $$ Answered by $@ty@m last updated on…
Question Number 183563 by CrispyXYZ last updated on 27/Dec/22 $$\mathrm{repost}\:\mathrm{an}\:\mathrm{unsolved}\:\mathrm{question}\:\mathrm{Q182552} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{period}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}: \\ $$$$\:{a}\bullet\:\mathrm{sin}\:\mathrm{4}{x}\:\mathrm{sin}\:\mathrm{3}{x} \\ $$$$\:{b}\bullet\:\mathrm{sin}\:\pi{x}+\:\mathrm{cos}\:{x} \\ $$$$\:{c}\bullet\:\frac{\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{3}{x}−\:\mathrm{3}\:\mathrm{tan}\:\mathrm{4}{x}+\:\mathrm{4}\:\mathrm{cot}\:\mathrm{6}{x}}{\mid\mathrm{cosec}\:\mathrm{8}{x}\mid−\:\mathrm{sec}^{\mathrm{3}} \:\mathrm{10}{x}+\:\sqrt{\mathrm{cot}\:\mathrm{12}{x}}} \\ $$ Commented by Acem…
Question Number 118019 by prakash jain last updated on 14/Oct/20 $$\mathrm{How}\:\mathrm{many}\:{n}\:\mathrm{digit}\:\mathrm{integers}\:\mathrm{are} \\ $$$$\mathrm{divisible}\:\mathrm{by}\:\mathrm{9}? \\ $$ Commented by prakash jain last updated on 14/Oct/20 $${d}_{\mathrm{1}} {d}_{\mathrm{2}}…