Question Number 43348 by peter frank last updated on 10/Sep/18 Answered by tanmay.chaudhury50@gmail.com last updated on 10/Sep/18 $$\left.\mathrm{3}\right)\mathrm{2}\left(\frac{{b}}{{a}}+\frac{{b}}{{c}}\right)=\frac{{a}}{{b}}+\frac{{a}}{{c}}+\frac{{c}}{{a}}+\frac{{c}}{{b}} \\ $$$${p}=\frac{{b}}{{a}}\:\:\:\:{q}=\frac{{b}}{{c}}\:\:\:\:\:\frac{{q}}{{p}}=\frac{{a}}{{c}} \\ $$$$\frac{{a}}{{q}}=\frac{{c}}{{p}}={r}\left({say}\right) \\ $$$${a}={rq} \\…
Question Number 174404 by Best1 last updated on 31/Jul/22 Answered by alephzero last updated on 31/Jul/22 $${F}\:'\left(\mathrm{2}\right)\:=\:\left({f}\:\circ\:{g}\right)'\left(\mathrm{2}\right)\:=\:{f}'\left({g}\left(\mathrm{2}\right)\right){g}'\left(\mathrm{2}\right)\:= \\ $$$$=\:{f}'\left(\mathrm{8}\right)×\mathrm{4}\:=\:\mathrm{6}×\mathrm{4}\:=\:\mathrm{24} \\ $$ Terms of Service Privacy…
Question Number 174406 by Best1 last updated on 31/Jul/22 Answered by alephzero last updated on 31/Jul/22 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{4}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }+\mathrm{2}\right)\:\mathrm{d}{x}\:= \\ $$$$\mathrm{4}\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}−{x}^{\mathrm{2}} \:}\mathrm{d}{x}\:+\int_{\mathrm{0}}…
Question Number 174396 by Best1 last updated on 31/Jul/22 Answered by som(math1967) last updated on 31/Jul/22 $${f}^{!} \left(\boldsymbol{{x}}\right)=\mathrm{2}.\mathrm{3}^{\boldsymbol{{mx}}} .\boldsymbol{{sec}}^{\mathrm{2}} \boldsymbol{{xtanx}}+{m}\mathrm{3}^{{mx}} {ln}\mathrm{3}{sec}^{\mathrm{2}} {x} \\ $$$$\Rightarrow\mathrm{0}+{mln}\mathrm{3}=\mathrm{3}\Rightarrow\boldsymbol{{m}}=\frac{\mathrm{3}}{\boldsymbol{{ln}}\mathrm{3}} \\…
Question Number 108854 by ZiYangLee last updated on 19/Aug/20 $$\mathrm{The}\:\mathrm{sixth}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.\:\mathrm{is}\:\mathrm{2},\:\mathrm{its} \\ $$$$\mathrm{common}\:\mathrm{difference}\:\mathrm{is}\:\mathrm{greater}\:\mathrm{than} \\ $$$$\mathrm{one}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{difference}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{first},\:\mathrm{fourth}\:\mathrm{and}\:\mathrm{fifth}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{greatest}. \\ $$ Answered by $@y@m…
Question Number 174389 by Best1 last updated on 31/Jul/22 $${what}\:{is}\:\:{least}\:{upper}\:{bound}\:{of}\:{the} \\ $$$${sequence}\:\left\{\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right){ln}\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)\right\}_{{n}=\mathrm{1}} ^{\infty} ? \\ $$$${A}.\mathrm{0}\:\:\:\:{B}.{ln}\mathrm{2}\:\:\:\:\:\:{C}.{ln}\mathrm{5}\:\:\:\:\:\:\:{D}.\mathrm{2}{ln}\mathrm{2}\: \\ $$ Answered by Gazella thomsonii last updated on…
Question Number 174376 by Best1 last updated on 31/Jul/22 $${if}\:{the}\:{mean}\:{of}\:{the}\:{data}\:\mathrm{1},\mathrm{2},\mathrm{3},\mathrm{4},…,\:\mathrm{100} \\ $$$$\:{is}\:\mathrm{50}.\mathrm{5}\:{then}\:{what}\:{is}\:{the}\:{mean}\:{of}\:{the}\: \\ $$$${data}\:\mathrm{5},\mathrm{7},\mathrm{9},\mathrm{11},…,\mathrm{203}?? \\ $$$$ \\ $$ Commented by Rasheed.Sindhi last updated on 31/Jul/22…
Question Number 174374 by Best1 last updated on 31/Jul/22 $${li}\underset{{x}\rightarrow\infty} {{m}}\left(\frac{{x}+\mathrm{3}}{{x}−\mathrm{2}}\right)^{{x}} \\ $$ Answered by LEKOUMA last updated on 31/Jul/22 $$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left[{f}\left({x}\right)\right]^{{g}\left({x}\right)} \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}{f}\left({x}\right)=\mathrm{1}\:{et}\:\underset{{x}\rightarrow\infty}…
Question Number 108815 by 1xx last updated on 19/Aug/20 $${f}\left({x}\right)=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}+\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{a}}}+\frac{\sqrt{{ax}}}{\:\sqrt{{ax}+\mathrm{8}}} \\ $$$${x}>\mathrm{0}\:,\:{a}>\mathrm{0}\:,\:{x}\in{R},\:{a}\in{R} \\ $$$${prove}:\mathrm{1}<{f}\left({x}\right)<\mathrm{2} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 108805 by ZiYangLee last updated on 19/Aug/20 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{sequence}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{be}\:\mathrm{1} \\ $$$$\mathrm{and}\:{r}.\: \\ $$$$\mathrm{If}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{satisfy}\:\mid{a}_{\mathrm{n}−\mathrm{1}} −{a}_{\mathrm{1}} \mid\leqslant\mid{a}_{\mathrm{n}} −{a}_{\mathrm{1}} \mid\:\mathrm{for} \\ $$$$\mathrm{all}\:\mathrm{n}\geqslant\mathrm{2},\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{r}. \\…