Question Number 206433 by universe last updated on 14/Apr/24 $$\:\:\:\:\:\mathrm{let}\:\mathrm{f}:\left[\mathrm{0},\infty\right)\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{continuous}\:\mathrm{function}\:\mathrm{if} \\ $$$$\:\:\:\:\underset{\mathrm{n}\rightarrow\infty\:} {\mathrm{lim}}\:\int_{\mathrm{0}} ^{\mathrm{1}} \mathrm{f}\left(\mathrm{x}+\mathrm{n}\right)\mathrm{dx}\:=\:\mathrm{2} \\ $$$$\:\mathrm{then}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{f}\left(\mathrm{nx}\right)\:=\:? \\ $$$$\: \\ $$ Answered by Berbere…
Question Number 206434 by MATHEMATICSAM last updated on 14/Apr/24 $$\mathrm{If}\:\mathrm{tan}^{\mathrm{2}} \theta\:=\:\mathrm{1}\:−\:{x}^{\mathrm{2}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{sec}\theta\:+\:\mathrm{tan}^{\mathrm{3}} \theta\mathrm{cosec}\theta\:=\:\sqrt{\left(\mathrm{2}\:−\:{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:. \\ $$ Answered by TonyCWX08 last updated on…
Question Number 206396 by cortano21 last updated on 13/Apr/24 Answered by mr W last updated on 13/Apr/24 Commented by mr W last updated on 13/Apr/24…
Question Number 206399 by BaliramKumar last updated on 13/Apr/24 Commented by mr W last updated on 14/Apr/24 $${since}\:{the}\:{question}\:{asks}\:{the}\:{ratio}\:{of} \\ $$$$“{their}''\:{speeds},\:{answers}\:\left({b}\right),\:\left({c}\right),\:\left({d}\right) \\ $$$${are}\:{all}\:{correct}. \\ $$$${when}\:{the}\:{question}\:{asks}\:{the}\:{ratio}\:{of} \\…
Question Number 206425 by hardmath last updated on 13/Apr/24 $$\mathrm{If}\:\:\:\mathrm{cos}\boldsymbol{\alpha}\:=\:\frac{\mathrm{3}}{\mathrm{5}}\:\:\:\left(\mathrm{0}<\boldsymbol{\alpha}<\frac{\boldsymbol{\pi}}{\mathrm{2}}\right) \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{tan}^{\mathrm{2}} \:\left(\mathrm{45}°\:+\:\frac{\boldsymbol{\alpha}}{\mathrm{2}}\right)}{\mathrm{3}}\:=\:? \\ $$ Answered by MM42 last updated on 13/Apr/24 $${tan}^{\mathrm{2}} {a}=\frac{\mathrm{1}−{cos}\mathrm{2}{a}}{\mathrm{1}+{cos}\mathrm{2}{a}} \\…
Question Number 206393 by MaruMaru last updated on 13/Apr/24 $$\mathrm{find}\:\mathrm{S}=\mathrm{1}+\underset{\ell} {\sum}\:\frac{\left(−\right)^{\ell} }{\ell}\left(\frac{\mathrm{1}}{\ell}−\frac{\mathrm{1}}{\ell+\mathrm{1}}\right)\:,\:\ell\in\left[\mathrm{1},\infty\right) \\ $$$$\mathrm{1}+\underset{\ell} {\sum}\:\frac{\left(−\right)^{\ell} }{\ell}\left(\frac{\mathrm{1}}{\ell}−\frac{\mathrm{1}}{\ell+\mathrm{1}}\right) \\ $$$$\mathrm{1}−\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\right)+\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{1}}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{3}}\right)−\frac{\mathrm{1}}{\mathrm{3}}\left(\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}\right)+\frac{\mathrm{1}}{\mathrm{4}}\left(\frac{\mathrm{1}}{\mathrm{4}}−\frac{\mathrm{1}}{\mathrm{5}}\right)−…… \\ $$ Answered by MaruMaru last updated…
Question Number 206394 by 0202391905769 last updated on 13/Apr/24 Commented by mr W last updated on 13/Apr/24 $$\Rightarrow{Q}\mathrm{206321} \\ $$ Terms of Service Privacy Policy…
Question Number 206421 by MATHEMATICSAM last updated on 13/Apr/24 $$\mathrm{If}\:\mathrm{tan}{p}\theta\:=\:{p}\mathrm{tan}\theta\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{sin}^{\mathrm{2}} {p}\theta}{\mathrm{sin}^{\mathrm{2}} \theta}\:=\:\frac{{p}^{\mathrm{2}} }{\mathrm{1}\:+\:\left({p}^{\mathrm{2}} \:−\:\mathrm{1}\right)\mathrm{sin}^{\mathrm{2}} \theta}\:.\: \\ $$ Answered by Frix last updated on…
Question Number 206391 by hardmath last updated on 13/Apr/24 $$\mathrm{Find}: \\ $$$$\int_{−\mathrm{3}} ^{\:−\mathrm{2}} \:\left(\mid\mathrm{x}\mid\:+\:\mid\mathrm{x}\:−\:\mathrm{4}\mid\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by MM42 last updated on 13/Apr/24 $${I}=\int_{−\mathrm{3}} ^{−\mathrm{2}}…
Question Number 206364 by Skabetix last updated on 12/Apr/24 Answered by TonyCWX08 last updated on 13/Apr/24 $${I}\:{only}\:{know} \\ $$$${e}^{\pi{i}} =−\mathrm{1} \\ $$$$\underset{−\infty} {\overset{\infty} {\int}}\frac{\mathrm{sin}\:\left({x}\right)}{{x}}\:{dx}\:=\:\pi \\…