Question Number 97972 by Aniruddha Ghosh last updated on 10/Jun/20 $$\:\:\:\:\mathrm{Prove}\:\mathrm{that}, \\ $$$$\:\:\:\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{e}}^{\boldsymbol{{x}}} \right)\:=\:\boldsymbol{{e}}^{\boldsymbol{{x}}} \\ $$ Answered by abdomathmax last updated on 10/Jun/20 $$\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{e}^{\mathrm{x}} \right)\:=\mathrm{lim}_{\mathrm{h}\rightarrow\mathrm{0}}…
Question Number 163510 by mnjuly1970 last updated on 07/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f} \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\mathrm{1}}{\:\sqrt{{sin}^{\:\mathrm{5}} \left({x}\right).{cos}\left({x}\right)}\:+\sqrt{{cos}^{\:\mathrm{5}} \left({x}\right).{sin}\left({x}\right)}}{dx}\:= \\ $$$$\:\:\:{find}\:{the}\:{value}\:{of}\:\::\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\:\right).\:\boldsymbol{\phi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…
Question Number 163487 by mnjuly1970 last updated on 07/Jan/22 $$ \\ $$$$\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{sin}^{\:\mathrm{2}} \left(\:\mathrm{ln}\left({x}\:\right)\right).\:\mathrm{ln}\:\left({x}\right)}{\:\sqrt{{x}}}\:{dx}=? \\ $$$$\:\:\:\:−−−−− \\ $$ Answered by Lordose last updated on…
Question Number 163400 by mnjuly1970 last updated on 06/Jan/22 $$ \\ $$$$\:\:\:\:\:{prove}\: \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\infty} {cot}^{\:−\mathrm{1}} \left(\mathrm{1}+{x}^{\:\mathrm{2}} \right)=\left(\sqrt{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{1}}{\mathrm{2}}}\:\right)\:\:\pi \\ $$$$ \\ $$ Answered by Ar…
Question Number 32316 by NECx last updated on 23/Mar/18 $${A}\:{gas}\:{expands}\:{according}\:{to}\:{the} \\ $$$${law}\:{pv}={constant},{where}\:{p}\:{is}\:{the} \\ $$$${pressure}\:{and}\:{v}\:{is}\:{the}\:{volume}\:{of} \\ $$$${the}\:{gas}.{Initially},{v}=\mathrm{1000}{m}^{\mathrm{3}} \:{and} \\ $$$${p}=\mathrm{40}{N}/{m}^{\mathrm{2}} .{If}\:{the}\:{pressure}\:{is} \\ $$$${decreased}\:{at}\:{the}\:{rate}\:{of}\:\mathrm{5}{Nm}^{−\mathrm{2}} {min}^{−\mathrm{1}} \\ $$$${find}\:{the}\:{rate}\:{at}\:{which}\:{the}\:{gas}\:{is}…
Question Number 32313 by NECx last updated on 23/Mar/18 $${If}\:{y}={sinx}\:{then}\:{show}\:{that} \\ $$$$\frac{{d}^{{n}} {y}}{{dx}^{{n}} }={sin}\left({x}+\frac{{n}\pi}{\mathrm{2}}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 32308 by Ruchinna1 last updated on 22/Mar/18 Answered by Joel578 last updated on 23/Mar/18 $$\left(\mathrm{3}\right) \\ $$$${y}''''\:=\:\mathrm{5}{x} \\ $$$$\:{y}'''\:=\:\frac{\mathrm{5}}{\mathrm{2}}{x}^{\mathrm{2}} \:+\:{C} \\ $$$$\:\:{y}''\:=\:\frac{\mathrm{5}}{\mathrm{6}}{x}^{\mathrm{3}} \:+\:{C}_{\mathrm{1}}…
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Question Number 32305 by abdo imad last updated on 22/Mar/18 $${find}\:\int_{\mathrm{1}} ^{{e}} \:{sin}\left({ln}\left({x}\right)\right){dx}\:. \\ $$ Commented by abdo imad last updated on 24/Mar/18 $${let}\:{use}\:{the}\:{ch}.{lnx}={t}\:\Rightarrow\:{I}\:=\:\int_{\mathrm{0}} ^{\mathrm{1}}…