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Category: Differentiation

In-the-given-equation-below-applying-the-formula-for-the-derivative-of-inverse-trigonometric-functions-what-is-the-u-from-the-given-function-y-cosec-1-sin-1-sin-x-cos-x-

Question Number 160933 by blackmamba last updated on 09/Dec/21 $$\:{In}\:{the}\:{given}\:{equation}\:{below}\:,\:{applying} \\ $$$${the}\:{formula}\:{for}\:{the}\:{derivative}\:{of} \\ $$$$\:{inverse}\:{trigonometric}\:{functions}\:, \\ $$$$\:{what}\:{is}\:{the}\:''{u}\:''\:{from}\:{the}\:{given}\:{function}. \\ $$$$\:{y}\:=\:\mathrm{cosec}^{−\mathrm{1}} \left[\:\mathrm{sin}\:\left(\frac{\mathrm{1}+\mathrm{sin}\:{x}}{\mathrm{cos}\:{x}}\right)\right] \\ $$ Answered by bobhans last…

f-x-1-lnx-1-x-1-1-lim-x-1-f-x-1-2-2-0-1-f-x-dx-

Question Number 95397 by ~blr237~ last updated on 25/May/20 $${f}\left({x}\right)=\frac{\mathrm{1}}{{lnx}}\:−\frac{\mathrm{1}}{{x}−\mathrm{1}}\: \\ $$$$\left.\mathrm{1}\right)\:\:\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:{f}\left({x}\right)=\frac{\mathrm{1}}{\mathrm{2}}\:\: \\ $$$$\left.\mathrm{2}\right)\:\:\:\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{f}\left({x}\right){dx}=\:\gamma\: \\ $$ Commented by Mikael_786 last updated on…

lim-n-1-n-HCF-20-n-0-

Question Number 95325 by ~blr237~ last updated on 24/May/20 $$\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\:\:\:\frac{\mathrm{1}}{{n}}{HCF}\left(\mathrm{20},{n}\right)\:=\:\mathrm{0}\:\:\:\:\:\:\:? \\ $$ Commented by mr W last updated on 24/May/20 $$\mathrm{1}\leqslant{HCF}\left(\mathrm{20},{n}\right)\leqslant\mathrm{20}\:{for}\:{n}\geqslant\mathrm{20} \\ $$$$\frac{\mathrm{1}}{{n}}\leqslant\frac{{HCF}\left(\mathrm{20},{n}\right)}{{n}}\leqslant\frac{\mathrm{20}}{{n}} \\…

lim-x-0-x-2x-ln-2-t-t-dt-ln2-2-

Question Number 95323 by ~blr237~ last updated on 24/May/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\int_{{x}} ^{\mathrm{2}{x}} \:\frac{{ln}\left(\mathrm{2}+{t}\right)}{{t}}{dt}\:=\:\left({ln}\mathrm{2}\right)^{\mathrm{2}} \\ $$ Answered by abdomathmax last updated on 24/May/20 $$\left.\exists\:\mathrm{c}\in\right]\mathrm{x},\mathrm{2x}\left[\:/\:\int_{\mathrm{x}} ^{\mathrm{2x}} \:\frac{\mathrm{ln}\left(\mathrm{2}+\mathrm{t}\right)}{\mathrm{t}}\mathrm{dt}\:=\mathrm{ln}\left(\mathrm{2}+\mathrm{c}\right)\int_{\mathrm{x}}…

Question-29778

Question Number 29778 by puneet1789 last updated on 12/Feb/18 Answered by Giannibo last updated on 12/Feb/18 $$ \\ $$$$ \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{1} \\ $$$$\mathrm{e}^{\mathrm{x}} \mathrm{f}\left(\mathrm{x}\right)+\mathrm{e}^{\mathrm{x}} \mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{e}^{\mathrm{x}}…

Question-160837

Question Number 160837 by mnjuly1970 last updated on 07/Dec/21 Commented by cortano last updated on 07/Dec/21 $$\Leftrightarrow\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{1}=\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right) \\ $$$$\Leftrightarrow\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{x}^{\mathrm{3}}…