Question Number 82125 by liki last updated on 18/Feb/20 Commented by john santu last updated on 18/Feb/20 $$\mathrm{log}_{{y}} \:\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{log}_{{x}} \:\left({y}\right)} \\ $$$$\Rightarrow\mathrm{log}_{{y}} \:\left({x}\right)\:+\:\frac{\mathrm{1}}{\mathrm{log}_{{y}} \left({x}\right)}\:=\:\mathrm{64} \\…
Question Number 82115 by Khyati last updated on 18/Feb/20 $${Q}.\:{Find}\:{the}\:{number}\:{of}\:{solution}\:{of}\:{thd} \\ $$$${equation}\:{tanx}\:+\:{secx}\:=\:\mathrm{2}\:{cosx}\:{lying}\:{in} \\ $$$${the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\pi\right]\:?? \\ $$ Answered by MJS last updated on 18/Feb/20 $$\mathrm{tan}\:{x}\:+\mathrm{sec}\:{x}\:=\mathrm{2cos}\:{x} \\…
Question Number 16572 by myintkhaing last updated on 24/Jun/17 Answered by Tinkutara last updated on 24/Jun/17 $$\left(\mathrm{i}\right)\:\mathrm{I}\:\mathrm{think}\:\mathrm{the}\:\mathrm{series}\:\mathrm{is}\:\mathrm{sin}^{\mathrm{2}} \:{x},\:\mathrm{sin}\:{x},\:\mathrm{1},\:… \\ $$$$\mathrm{It}\:\mathrm{is}\:\mathrm{a}\:\mathrm{G}.\mathrm{P}.\:\mathrm{with}\:\mathrm{common}\:\mathrm{ratio} \\ $$$$\mathrm{cosec}\:{x}. \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{7}^{\mathrm{th}} \:\mathrm{term}\:=\:{ar}^{\mathrm{6}}…
Question Number 147635 by tabata last updated on 22/Jul/21 $${find}\:{the}\:{taylor}\:{series}\:{f}\left({z}\right)={cosz}\:\:,{z}=\frac{\pi}{\mathrm{4}} \\ $$$$ \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on 22/Jul/21…
Question Number 147612 by ZiYangLee last updated on 22/Jul/21 $$\mathrm{Given}\:\mathrm{that}\:{f}\left({x}\right)=\frac{\left({x}^{\mathrm{3}} +\mathrm{1}\right)^{\mathrm{2}} \sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{\mathrm{1}+\sqrt{{x}}}. \\ $$$$\mathrm{By}\:\mathrm{using}\:\mathrm{logarithmatic}\:\mathrm{differentiation}, \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{f}\:'\left(\mathrm{1}\right). \\ $$ Answered by mathmax by abdo last…
Question Number 147593 by 0731619 last updated on 22/Jul/21 Answered by gsk2684 last updated on 22/Jul/21 $${put}\:\mathrm{sin}\:{y}\:=\:{t}\Rightarrow\mathrm{cos}\:{y}\:{dy}\:=\:{dt} \\ $$$$\int\frac{\mathrm{1}}{{t}^{\mathrm{2}} +{t}−\mathrm{6}}{dt}=\int\frac{\mathrm{1}}{\left({t}−\mathrm{2}\right)\left({t}+\mathrm{3}\right)}{dt} \\ $$$$=\int\left(\frac{\frac{\mathrm{1}}{\mathrm{5}}}{{t}−\mathrm{2}}+\frac{−\frac{\mathrm{1}}{\mathrm{5}}}{{t}+\mathrm{3}}\right){dt} \\ $$$$=\frac{\mathrm{1}}{\mathrm{5}}\left(\mathrm{ln}\:\left({t}−\mathrm{2}\right)−\mathrm{ln}\:\left({t}+\mathrm{3}\right)\right)+{c} \\…
Question Number 16528 by I’m a gamer last updated on 23/Jun/17 Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 24/Jun/17 $$\mathrm{3}\left({a}+{b}+{c}\right)−\frac{{a}}{{b}}−\frac{{b}}{{c}}−\frac{{c}}{{a}}\leqslant\mathrm{6} \\ $$$$\mathrm{3}\geqslant\mathrm{3}\sqrt[{\mathrm{3}}]{{abc}\sqrt{{abc}}}=\mathrm{3}\left({abc}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \Rightarrow{abc}\leqslant\mathrm{1} \\ $$$${a}+{b}+{c}\leqslant\mathrm{3}\sqrt[{\mathrm{3}}]{{abc}}\leqslant\mathrm{3} \\…
Question Number 147573 by phally last updated on 22/Jul/21 Commented by phally last updated on 22/Jul/21 $$\:\mathrm{help}\:\mathrm{me}? \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 147569 by Sozan last updated on 21/Jul/21 $${find}\:{the}\:{taylor}\:{series}\:{of}\:{f}\left({z}\right)={sinz}\:,{z}=\frac{\pi}{\mathrm{4}}\:{in}\:{complex}\:{number} \\ $$ Answered by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{f}\left(\mathrm{z}\right)=\sum_{\mathrm{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{f}^{\left(\mathrm{n}\right)} \left(\frac{\pi}{\mathrm{4}}\right)}{\mathrm{n}!}\left(\mathrm{z}−\frac{\pi}{\mathrm{4}}\right)^{\mathrm{n}}…
Question Number 16501 by gokux2123 last updated on 23/Jun/17 $$\mathrm{3}+\mathrm{3} \\ $$ Answered by Tinkutara last updated on 23/Jun/17 $$\mathrm{3}\:+\:\mathrm{3}\:=\:\mathrm{6} \\ $$ Terms of Service…