Question Number 23711 by Tinkutara last updated on 04/Nov/17 $$\mathrm{A}\:\mathrm{certain}\:\mathrm{ideal}\:\mathrm{gas}\:\mathrm{has}\:\mathrm{C}_{\mathrm{v},\:\mathrm{m}} \:=\:\mathrm{a}\:+\:\mathrm{bT}, \\ $$$$\mathrm{where}\:\mathrm{a}\:=\:\mathrm{25}\:\mathrm{J}/\left(\mathrm{mol}.\:\mathrm{K}\right)\:\mathrm{and}\:\mathrm{b}\:=\:\mathrm{0}.\mathrm{03} \\ $$$$\mathrm{J}\left(\mathrm{mol}.\mathrm{K}^{\mathrm{2}} \right).\:\mathrm{Let}\:\mathrm{2}\:\mathrm{mole}\:\mathrm{of}\:\mathrm{this}\:\mathrm{gas}\:\mathrm{go} \\ $$$$\mathrm{from}\:\mathrm{300}\:\mathrm{K}\:\mathrm{and}\:\mathrm{2}\:\mathrm{litre}\:\mathrm{volume}\:\mathrm{to}\:\mathrm{600}\:\mathrm{K} \\ $$$$\mathrm{and}\:\mathrm{4}\:\mathrm{litre}.\:\Delta\mathrm{S}_{\mathrm{gas}} \:\mathrm{is} \\ $$ Answered by…
Question Number 154780 by talminator2856791 last updated on 21/Sep/21 $$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\int_{−\infty} ^{\:\infty} \:\frac{\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$\: \\ $$ Answered by phanphuoc last…
Question Number 89244 by 174 last updated on 16/Apr/20 Commented by mathmax by abdo last updated on 16/Apr/20 $${A}\:=\int_{\mathrm{0}} ^{\mathrm{1}} \left\{\frac{\mathrm{1}}{{x}}\right\}^{\mathrm{2}} \:{dx}\:\:{cha}\mathrm{7}{gement}\:\frac{\mathrm{1}}{{x}}={t}\:{give}\: \\ $$$${A}\:=−\int_{\mathrm{1}} ^{+\infty}…
Question Number 154777 by Khalmohmmad last updated on 21/Sep/21 Answered by john_santu last updated on 21/Sep/21 $${it}\:{should}\:{be}\:\underset{{k}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\frac{{k}^{\mathrm{2}} −\mathrm{25}}{{k}−\mathrm{5}}\right)={k}+\mathrm{5} \\ $$$${or}\:{if}\:\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\frac{{k}^{\mathrm{2}} −\mathrm{25}}{{k}−\mathrm{5}}\right)=\left(\frac{{k}^{\mathrm{2}} −\mathrm{25}}{{k}−\mathrm{5}}\right)×\underset{{x}\rightarrow\mathrm{5}} {\mathrm{lim}}\left(\mathrm{1}\right)…
Question Number 23707 by Tinkutara last updated on 04/Nov/17 $$\mathrm{Two}\:\mathrm{blocks}\:{A}\:\mathrm{and}\:{B}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{1}\:\mathrm{kg}\:\mathrm{and} \\ $$$$\mathrm{2}\:\mathrm{kg}\:\mathrm{respectively}\:\mathrm{are}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a} \\ $$$$\mathrm{string},\:\mathrm{passing}\:\mathrm{over}\:\mathrm{a}\:\mathrm{light}\:\mathrm{frictionless} \\ $$$$\mathrm{pulley}.\:\mathrm{Both}\:\mathrm{the}\:\mathrm{blocks}\:\mathrm{are}\:\mathrm{resting}\:\mathrm{on}\:\mathrm{a} \\ $$$$\mathrm{horizontal}\:\mathrm{floor}\:\mathrm{and}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{is}\:\mathrm{held} \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{string}\:\mathrm{remains}\:\mathrm{just}\:\mathrm{taut}.\:\mathrm{At} \\ $$$$\mathrm{time}\:{t}\:=\:\mathrm{0},\:\mathrm{a}\:\mathrm{force}\:{F}\:=\:\mathrm{20}{t}\:\mathrm{N},\:\mathrm{starts} \\ $$$$\mathrm{acting}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pulley}\:\mathrm{along}\:\mathrm{vertically} \\…
Question Number 154776 by john_santu last updated on 21/Sep/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{1}+\frac{\mathrm{1}−\frac{\mathrm{sin}\:\left(\frac{\mathrm{1}}{{x}}\right)}{\frac{\mathrm{1}}{{x}}}}{{e}−\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} }\right)^{{x}} =? \\ $$ Commented by mathdanisur last updated on 21/Sep/21 $$\mathrm{say}\:\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{t}\:\Rightarrow\:\mathrm{t}\rightarrow\mathrm{0} \\ $$$$\mathrm{e}^{\underset{\boldsymbol{\mathrm{t}}\rightarrow\mathrm{0}}…
Question Number 89243 by M±th+et£s last updated on 16/Apr/20 $${solve}\:{the}\:{following}\:{diffirntial}\:{equation} \\ $$$$\left.\mathrm{1}\right)\left(\mathrm{2}{x}+{y}\right){dx}+\left({x}+{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{3}{x}−{y}\right){dx}−\left({x}−{y}\right){dy}=\mathrm{0} \\ $$$$\left.\mathrm{3}\right)\:\left({cos}\left({x}\right)+{y}\right){dx}\:+\:\left(\mathrm{2}{y}+{x}\right){dy}=\mathrm{0} \\ $$ Answered by TANMAY PANACEA. last updated on…
Question Number 89240 by Ar Brandon last updated on 16/Apr/20 $${If}\:{I}_{{n}} =\int_{\mathrm{0}} ^{\pi} {e}^{{x}} {sin}^{{n}} {xdx},\:{show}\:{that}\: \\ $$$$\left({n}^{\mathrm{2}} +\mathrm{1}\right){I}_{{n}} ={n}\left({n}−\mathrm{1}\right){I}_{{n}−\mathrm{2}} \\ $$ Terms of Service…
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Question Number 89238 by cindiaulia last updated on 16/Apr/20 $$\int_{\mathrm{7}} ^{\mathrm{12}} \mathrm{x}^{\mathrm{2}} \sqrt{\mathrm{x}−\mathrm{3}} \\ $$ Commented by mathmax by abdo last updated on 16/Apr/20 $${I}=\int\:{x}^{\mathrm{2}}…