Question Number 197338 by yusufkhabibulloh last updated on 13/Sep/23 $$\int\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$ Answered by TheHoneyCat last updated on 13/Sep/23 $$=\int\frac{{x}^{\mathrm{2}} +\mathrm{1}−\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{d}{x} \\…
Question Number 197301 by uchihayahia last updated on 13/Sep/23 $$ \\ $$$$\:{how}\:{do}\:{i}\:{calculate}\:{this} \\ $$$$\:\underset{{x}\rightarrow-\infty} {\mathrm{lim}}\:\frac{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{2}}{{x}^{\mathrm{3}} +\mathrm{2}{x}^{\mathrm{2}} +{x}−\mathrm{1}} \\ $$$$\:{multiplying}\:{both}\:{numerator} \\ $$$$\:{and}\:{denumerator}\:{by}\:\frac{\mathrm{1}}{{x}^{\mathrm{4}} } \\…
Question Number 197335 by sonukgindia last updated on 13/Sep/23 Answered by witcher3 last updated on 13/Sep/23 $$\mathrm{x}\rightarrow\frac{\mathrm{1}}{\mathrm{x}} \\ $$$$\mathrm{I}=\int_{\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}}} ^{\sqrt{\mathrm{3}}} \frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{tan}^{−\mathrm{1}} \left(\frac{\sqrt{\mathrm{3}}\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{2}}\right)\mathrm{dx}…
Question Number 197325 by sonukgindia last updated on 13/Sep/23 Answered by witcher3 last updated on 13/Sep/23 $$\mathrm{f}\left(\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} −\mathrm{1} \\ $$$$\mathrm{if}\:\mathrm{x}\in\mathbb{R}\:\mid\mathrm{f}^{\mathrm{2}} \left(\mathrm{x}\right)=\mathrm{x}\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{x}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{x}\in\left\{\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}},\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}\right\} \\…
Question Number 197327 by mnjuly1970 last updated on 13/Sep/23 $$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{trigonometry}… \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{P}\:=\:\underset{{k}=\mathrm{1}} {\overset{\mathrm{44}} {\prod}}\left(\:\:\mathrm{1}\:+\:{tan}\left({k}\right)\:\right)\:=\:?\:\: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$ Answered…
Question Number 197320 by tri26112004 last updated on 13/Sep/23 $$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\right)^{{k}\left({k}+\mathrm{1}\right)} \\ $$ Answered by Erico last updated on 13/Sep/23 $$\forall\mathrm{k}\in\left[\mathrm{1},\mathrm{n}\right]\:\:\:\:\:\left(−\mathrm{1}\right)^{\mathrm{k}\left(\mathrm{k}+\mathrm{1}\right)} =\mathrm{1} \\ $$$$\Rightarrow\:\underset{\mathrm{k}=\mathrm{1}}…
Question Number 197323 by Erico last updated on 13/Sep/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\frac{\mathrm{sin}\left(\mathrm{x}\right)}{\mathrm{x}}\:\:\:\mathrm{and}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\left[\mathrm{f}\left(\mathrm{k}\pi+\frac{\pi}{\alpha}\right)+\mathrm{f}\left(\mathrm{k}\pi−\frac{\pi}{\alpha}\right)\right]\:\:\:\:\left(\alpha>\mathrm{1}\right) \\ $$$$\mathrm{Prove}\:\mathrm{that}\:\underset{\mathrm{n}\rightarrow+\infty} {\:\mathrm{lim}}\:\mathrm{S}_{\mathrm{n}} \left(\alpha\right)=\mathrm{1}−\mathrm{f}\left(\frac{\pi}{\alpha}\right) \\ $$ Answered by witcher3 last updated on…
Question Number 197317 by universe last updated on 13/Sep/23 $$\:\mathrm{if}\:\:\:\mathrm{x}\:\:=\:\:\frac{\mathrm{cos}\:\theta}{\mathrm{u}}\:\:,\:\mathrm{y}\:\:=\:\frac{\mathrm{sin}\:\theta}{\mathrm{u}}\:\:{and}\:\mathrm{z}\:\:=\:\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right) \\ $$$$\mathrm{then}\:\mathrm{show}\:\mathrm{that}\: \\ $$$$\:\:\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{x}^{\mathrm{2}} }\:+\:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{y}^{\mathrm{2}} }\:=\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\mathrm{u}^{\mathrm{2}} }\:+\:\mathrm{u}^{\mathrm{3}} \:\frac{\partial\mathrm{z}}{\partial\mathrm{u}}\:+\:\mathrm{u}^{\mathrm{4}} \:\frac{\partial^{\mathrm{2}} \mathrm{z}}{\partial\theta^{\mathrm{2}} }…
Question Number 197312 by mathlove last updated on 13/Sep/23 $$\frac{\left({log}_{\mathrm{2}} \mathrm{20}\right)^{\mathrm{2}} −\left({log}_{\mathrm{2}} \mathrm{5}\right)^{\mathrm{2}} }{{log}_{\mathrm{2}} \mathrm{10}}=? \\ $$ Answered by som(math1967) last updated on 13/Sep/23 $$\mathrm{4}…
Question Number 197277 by Sachinkhar last updated on 12/Sep/23 Answered by Sachinkhar last updated on 12/Sep/23 $$\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{anybody}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}} \\ $$ Terms of Service Privacy Policy Contact:…