Question Number 202490 by Calculusboy last updated on 27/Dec/23 Commented by aleks041103 last updated on 27/Dec/23 $${is}\:\left\{{x}\right\}\:{the}\:{whole}\:{part}\:{or}\:{the}\:{fractional}\:{part}? \\ $$ Commented by Calculusboy last updated on…
Question Number 202459 by MATHEMATICSAM last updated on 27/Dec/23 $$\mathrm{If}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{two}\:\mathrm{roots}\:\mathrm{of}\: \\ $$$${x}^{\mathrm{2}} \:−\:{lx}\:+\:{m}\:=\:\mathrm{0}\:\mathrm{is}\:\mathrm{1}\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${l}^{\mathrm{2}} \:+\:\mathrm{4}{m}^{\mathrm{2}} \:=\:\left(\mathrm{1}\:+\:\mathrm{2}{m}\right)^{\mathrm{2}} \:. \\ $$ Answered by aleks041103 last updated…
Question Number 202485 by Calculusboy last updated on 27/Dec/23 Commented by MathematicalUser2357 last updated on 28/Dec/23 $$\mathrm{Can}'\mathrm{t}\:\mathrm{integrate}\:\mathrm{in}\:\mathrm{range}\:\left[−\infty,\:\infty\right] \\ $$ Commented by TheHoneyCat last updated on…
Question Number 202477 by MATHEMATICSAM last updated on 27/Dec/23 $$\mathrm{If}\:{x}\:=\:\frac{\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} }\:+\:\sqrt{{a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} }}{\:\sqrt{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} }\:−\:\sqrt{{a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} }}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${b}^{\mathrm{2}} {x}^{\mathrm{2}} \:−\:\mathrm{2}{a}^{\mathrm{2}} {x}\:+\:{b}^{\mathrm{2}} \:=\:\mathrm{0}. \\…
Question Number 202473 by hardmath last updated on 27/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:\centerdot\:\mathrm{n}!}{\left(\mathrm{2n}\right)!}\:\:\:\:\:\:\:\:\:\:\mathrm{2}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(\mathrm{x}\:+\:\mathrm{5}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{3}^{\boldsymbol{\mathrm{n}}+\mathrm{1}} \:\centerdot\:\mathrm{n}\:\centerdot\:\mathrm{ln}\left(\mathrm{n}\right)} \\ $$ Terms of Service Privacy…
Question Number 202468 by hardmath last updated on 27/Dec/23 $$\mathrm{Find}: \\ $$$$\mathrm{1}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\:\infty} {\sum}}\:\frac{\mathrm{16}}{\mathrm{16n}^{\mathrm{2}} \:−\:\mathrm{8n}\:−\:\mathrm{3}}\:=\:?\:\:\:\:\:\mathrm{2}.\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\:\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} }{\mathrm{2n}^{\mathrm{3}} }\:=\:? \\ $$ Answered by Rasheed.Sindhi last…
Question Number 202464 by hardmath last updated on 27/Dec/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 202466 by Rydel last updated on 27/Dec/23 $$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\frac{{x}\sqrt{\mathrm{ln}\:\left({x}^{\mathrm{2}} +\mathrm{1}\right)}}{\mathrm{1}+{e}^{{x}−\mathrm{3}} } \\ $$ Answered by Mathspace last updated on 27/Dec/23 $$={lim}_{{x}\rightarrow+\infty} {xe}^{−{x}+\mathrm{3}} \sqrt{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 202392 by MATHEMATICSAM last updated on 26/Dec/23 $$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{b}\:=\:\mathrm{0} \\ $$$$\mathrm{is}\:{p}\::\:{q}\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$$\sqrt{\frac{{p}}{{q}}}\:+\:\sqrt{\frac{{q}}{{p}}}\:+\:\sqrt{\frac{{b}}{{a}}}\:=\:\mathrm{0}. \\ $$ Commented by MATHEMATICSAM last updated on 26/Dec/23 $$\mathrm{The}\:\mathrm{question}\:\mathrm{is}\:\mathrm{corrected}\:\mathrm{now}…
Question Number 202393 by sonukgindia last updated on 26/Dec/23 Answered by Mathspace last updated on 26/Dec/23 $${I}=\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{{a}+{bx}^{\mathrm{2}} }{dx}\:\:\:\:\:\:\:\:\:\left({a}>\mathrm{0},{b}>\mathrm{0}\right) \\ $$$${I}=\frac{\mathrm{1}}{{a}}\int_{\mathrm{0}} ^{\infty} \frac{{lnx}}{\mathrm{1}+\frac{{b}}{{a}}{x}^{\mathrm{2}} }{dx}\:\:\left(\sqrt{\frac{{b}}{{a}}}{x}={t}\right)…