Question Number 141779 by iloveisrael last updated on 23/May/21 $$\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}^{\mathrm{2}} }{{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{1}+{x}}}\:=? \\ $$ Answered by Willson last updated on 23/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{x}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{1}+\mathrm{x}}}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2x}}{\mathrm{1}−\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+\mathrm{x}}}}…
Question Number 10705 by Saham last updated on 23/Feb/17 $$\mathrm{A}\:\mathrm{pipe}\:\mathrm{closed}\:\mathrm{at}\:\mathrm{one}\:\mathrm{end}\:\mathrm{emits}\:\mathrm{sound}\:\mathrm{waves}\:\mathrm{of}\:\mathrm{frequency}\:\mathrm{440Hz}.\: \\ $$$$\mathrm{Determine}\:\left(\mathrm{i}\right)\:\mathrm{The}\:\mathrm{lenght}\:\mathrm{of}\:\mathrm{air}\:\mathrm{column}\:\: \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{The}\:\mathrm{frequencies}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{second}\:\mathrm{overtones}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 10704 by Saham last updated on 23/Feb/17 $$\mathrm{If}\:\mathrm{the}\:\mathrm{bulk}\:\mathrm{modulus}\:\mathrm{for}\:\mathrm{water}\:\mathrm{is}\:\mathrm{2}.\mathrm{28}\:×\:\mathrm{10}^{\mathrm{9}} \mathrm{Nm}^{−\mathrm{2}} \:,\:\mathrm{determine}\:\mathrm{the}\: \\ $$$$\mathrm{time}\:\mathrm{it}\:\mathrm{takes}\:\mathrm{for}\:\mathrm{a}\:\mathrm{sound}\:\mathrm{to}\:\mathrm{travel}\:\mathrm{a}\:\mathrm{distant}\:\mathrm{of}\:\mathrm{110m}\:\mathrm{in}\:\mathrm{water}\:\mathrm{of}\: \\ $$$$\mathrm{density}\:\mathrm{1000kgm}^{−\mathrm{3}} . \\ $$ Answered by ridwan balatif last updated…
Question Number 141775 by mathmax by abdo last updated on 23/May/21 $$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by qaz last updated…
Question Number 141774 by mathmax by abdo last updated on 23/May/21 $$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{e}^{−\mathrm{x}^{\mathrm{2}} } }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }\mathrm{dx} \\ $$ Answered by Dwaipayan Shikari last updated…
Question Number 141769 by 7770 last updated on 23/May/21 $$\boldsymbol{\mathrm{If}}\:\:\boldsymbol{\mathrm{y}}=\mathrm{2}\boldsymbol{\mathrm{sinx}}+\boldsymbol{\mathrm{tanx}},\:\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }=\mathrm{2}\boldsymbol{\mathrm{sinx}}\left(\boldsymbol{\mathrm{sec}}^{\mathrm{3}} \boldsymbol{\mathrm{x}}−\mathrm{1}\right) \\ $$$$\boldsymbol{\mathrm{Any}}\:\boldsymbol{\mathrm{detailed}}\:\boldsymbol{\mathrm{solution}}\:\boldsymbol{\mathrm{please}}. \\ $$ Answered by physicstutes last updated on…
Question Number 141768 by loveineq last updated on 23/May/21 $$\mathrm{Let}\:{a},{b},{x},{y}\:>\:\mathrm{0}\:\mathrm{and}\:\left({a}+{x}\right)\left({b}+{y}\right)\:=\:\left({a}+{b}\right)^{\mathrm{2}} \:.\:\:\:\:\:\:\:\: \\ $$$$\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}−{y}}{{x}}+\frac{{b}−{x}}{{y}}\:\leqslant\:\frac{{b}−{x}}{{a}}+\frac{{a}−{y}}{{b}}\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 76232 by Rio Michael last updated on 25/Dec/19 $${how}\:{do}\:{we}\:{find} \\ $$$$\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\:{sinh}^{−\mathrm{1}} {x}\:{dx}\:{and}\:\:\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}\mathrm{cosh}\:^{−\mathrm{1}} {xdx} \\ $$ Commented by mr W…
Question Number 10696 by okhema last updated on 23/Feb/17 $${given}\:{that}\:{tan}\mathrm{2}{x}=\frac{\mathrm{1}}{\mathrm{4}}{and}\:{that}\:{angle}\:{x}\:{is}\:{acute},\:{calculate},{without}\:{using}\:{a}\:{calculator}\:{the}\:{value}\:{of}\:{these}. \\ $$$$\left({a}\right)\:{cos}\mathrm{2}{x} \\ $$$$\left({b}\right)\:{sinx} \\ $$$$ \\ $$ Answered by mrW1 last updated on 23/Feb/17…
Question Number 10695 by okhema last updated on 23/Feb/17 $${prove}\:{that}\:{tanx}−{cotx}=−\mathrm{2}{cot}\mathrm{2}{x} \\ $$ Answered by nume1114 last updated on 23/Feb/17 $$\:\:\:\:\mathrm{tan}\:{x}−\mathrm{cot}\:{x} \\ $$$$=\frac{\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}−\frac{\mathrm{cos}\:{x}}{\mathrm{sin}\:{x}} \\ $$$$=\frac{\mathrm{sin}^{\mathrm{2}} {x}−\mathrm{cos}^{\mathrm{2}}…