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Category: Differentiation

0-1-Li-2-x-2-dx-m-n-

Question Number 163682 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\:\:\Omega=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \:\left(\mathrm{Li}_{\:\mathrm{2}} ^{\:} \left({x}\:\right)\right)^{\:\mathrm{2}} {dx}\:=\:?\:\:\:\:\:\:\blacksquare\:{m}.{n}\:\:\: \\ $$$$\:\:\:\:\:−−−\:−−− \\ $$$$\:\:\:\: \\ $$ Answered by…

Prove-that-d-dx-e-x-e-x-

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}}…

If-0-pi-2-1-sin-5-x-cos-x-cos-5-x-sin-x-dx-find-the-value-of-2-3-4-

Question Number 163510 by mnjuly1970 last updated on 07/Jan/22 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f} \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\mathrm{1}}{\:\sqrt{{sin}^{\:\mathrm{5}} \left({x}\right).{cos}\left({x}\right)}\:+\sqrt{{cos}^{\:\mathrm{5}} \left({x}\right).{sin}\left({x}\right)}}{dx}\:= \\ $$$$\:\:\:{find}\:{the}\:{value}\:{of}\:\::\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\:\right).\:\boldsymbol{\phi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…

A-gas-expands-according-to-the-law-pv-constant-where-p-is-the-pressure-and-v-is-the-volume-of-the-gas-Initially-v-1000m-3-and-p-40N-m-2-If-the-pressure-is-decreased-at-the-rate-of-5Nm-2-min-1-

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}…