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 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and}\:\mathrm{the}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{sequence}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{be}\:\mathrm{1} \\ $$$$\mathrm{and}\:{r}.\: \\ $$$$\mathrm{If}\:\left\{{a}_{\mathrm{n}} \right\}\:\mathrm{satisfy}\:\mid{a}_{\mathrm{n}−\mathrm{1}} −{a}_{\mathrm{1}} \mid\leqslant\mid{a}_{\mathrm{n}} −{a}_{\mathrm{1}} \mid\:\mathrm{for} \\ $$$$\mathrm{all}\:\mathrm{n}\geqslant\mathrm{2},\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:{r}. \\…
Question Number 108787 by 150505R last updated on 19/Aug/20 Answered by Dwaipayan Shikari last updated on 19/Aug/20 $$\mathrm{1}−\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{8}{n}−\mathrm{1}}+\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{8}{n}+\mathrm{1}} \\ $$$$\mathrm{1}+\underset{{n}=\mathrm{1}} {\overset{\infty}…
Question Number 108766 by bemath last updated on 19/Aug/20 $$\:\:\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\bigstar} \\ $$$$\left(\mathrm{1}\right)\:{find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{line}\:{to} \\ $$$${the}\:{graph}\:{of}\:{the}\:{equation}\:\mathrm{sin}^{−\mathrm{1}} \left({x}\right)+\mathrm{cos}^{−\mathrm{1}} \left({y}\right)=\frac{\pi}{\mathrm{2}} \\ $$$${at}\:{given}\:{point}\:\left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}},\:\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right){If}\:{f}\left({x}\right)=\:\underset{{t}\rightarrow{x}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:{t}−\mathrm{sec}\:{x}}{{t}−{x}}\:,\:{find}\:{the}\:{value}\:{of}\: \\ $$$${f}\:'\left(\frac{\pi}{\mathrm{4}}\right) \\ $$$$\left(\mathrm{3}\right)\:\underset{{x}\rightarrow\mathrm{1}}…
Question Number 174292 by akolade last updated on 29/Jul/22 $$\frac{\mathrm{log}\left(\sqrt{\mathrm{x}+\mathrm{1}}+\mathrm{1}\right)}{\mathrm{log}^{\mathrm{3}} \sqrt{\mathrm{x}−\mathrm{40}}}=\mathrm{3} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$ Answered by Rasheed.Sindhi last updated on 29/Jul/22 $$\frac{\mathrm{log}\left(\sqrt{\mathrm{x}+\mathrm{1}}+\mathrm{1}\right)}{\mathrm{log}^{\mathrm{3}} \sqrt{\mathrm{x}−\mathrm{40}}}=\mathrm{3} \\…
Question Number 174291 by akolade last updated on 29/Jul/22 $$\mathrm{Find} \\ $$$$\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}} \\ $$$$\mathrm{if}\:\mathrm{log}\left(\frac{\mathrm{x}+\mathrm{y}}{\mathrm{3}}\right)=\frac{\mathrm{logx}+\mathrm{logy}}{\mathrm{2}} \\ $$ Answered by Rasheed.Sindhi last updated on 29/Jul/22 $$\mathrm{log}\left(\frac{\mathrm{x}+\mathrm{y}}{\mathrm{3}}\right)=\frac{\mathrm{logx}+\mathrm{logy}}{\mathrm{2}}\:;\:\frac{\mathrm{x}}{\mathrm{y}}+\frac{\mathrm{y}}{\mathrm{x}}=? \\…