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Category: Differentiation

Question-98213

Question Number 98213 by me2love2math last updated on 12/Jun/20 Commented by bemath last updated on 12/Jun/20 $$\mathrm{let}\:\frac{\mathrm{1}}{\mathrm{x}}\:=\:\mathrm{t}\:,\:\mathrm{t}\:\rightarrow\mathrm{0}\: \\ $$$$\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{3}{t}\right)}{{t}}\:=\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3t}}}{\mathrm{1}}\:=\:\frac{\mathrm{3}}{\mathrm{1}}=\mathrm{3} \\ $$ Answered by…

If-sin-x-ln-2-x-x-then-find-Im-m-n-

Question Number 163732 by mnjuly1970 last updated on 09/Jan/22 $$ \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:\mathrm{I}{f}\:,\:\:\boldsymbol{\phi}\:=\:\int_{−\infty} ^{\:+\infty} \frac{\:{sin}\left({x}\right).{ln}^{\:\mathrm{2}} \left({x}\:\right)}{{x}}\:\:{then} \\ $$$$\:\:\:\:\:\:{find}\:\::\:\:\:\:\:\:\:\:\:\mathcal{I}{m}\:\left(\boldsymbol{\phi}\:\right)\:=\:?\:\:\:\:\:\:\:\:\:\:\blacksquare\:{m}.{n}\: \\ $$$$ \\ $$ Terms of…

K-x-3-cos-x-5-4sin-x-max-K-x-min-K-x-

Question Number 163700 by blackmamba last updated on 09/Jan/22 $$\:\:\mathcal{K}\left({x}\right)\:=\:\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4sin}\:{x}} \\ $$$$\:\left.\begin{matrix}{{max}\:\mathcal{K}\left({x}\right)}\\{{min}\:\mathcal{K}\left({x}\right)}\end{matrix}\right\}\:=? \\ $$ Answered by mr W last updated on 10/Jan/22 $$\frac{\mathrm{3}\:\mathrm{cos}\:{x}}{\mathrm{5}+\mathrm{4}\:\mathrm{sin}\:{x}}={k} \\ $$$$\mathrm{3}\:\mathrm{cos}\:{x}−\mathrm{4}{k}\:\mathrm{sin}\:{x}=\mathrm{5}{k}…

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 $$ \\ $$$$\:\:\:\:\:\:\mathrm{I}{f} \\ $$$$\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{\:\mathrm{1}}{\:\sqrt{{sin}^{\:\mathrm{5}} \left({x}\right).{cos}\left({x}\right)}\:+\sqrt{{cos}^{\:\mathrm{5}} \left({x}\right).{sin}\left({x}\right)}}{dx}\:= \\ $$$$\:\:\:{find}\:{the}\:{value}\:{of}\:\::\:\Gamma^{\:\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\:\right).\:\boldsymbol{\phi} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$…