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Category: Differentiation

let-f-x-arctan-nx-with-n-integr-natural-1-calculate-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-

Question Number 62809 by mathmax by abdo last updated on 25/Jun/19 $${let}\:{f}\left({x}\right)\:=\:{arctan}\left({nx}\right)\:\:\:{with}\:{n}\:{integr}\:{natural} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by mathmax by abdo…

1-e-dx-x-ln-x-1-3-

Question Number 128279 by liberty last updated on 06/Jan/21 $$\:\:\Theta\:=\:\int_{\mathrm{1}} ^{\:\mathrm{e}} \:\frac{{dx}}{{x}.\sqrt[{\mathrm{3}}]{\mathrm{ln}\:{x}}}\:?\: \\ $$ Answered by john_santu last updated on 06/Jan/21 $$\:{let}\:\sqrt[{\mathrm{3}\:}]{\mathrm{ln}\:{x}}\:=\:{w}\:\Rightarrow\:\frac{{dx}}{{x}}\:=\:\mathrm{3}{w}^{\mathrm{2}} \:{dw} \\ $$$$\:\Theta\:=\:\int_{\mathrm{0}}…

nice-calculus-prove-that-0-pi-tan-1-tan-2-x-tan-2-x-dx-pi-2-pi-4-

Question Number 128225 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{prove}\:\:{that}\:: \\ $$$$\:\:\:\phi\:=\:\int_{\mathrm{0}} ^{\:\pi} \frac{{tan}^{−\mathrm{1}} \left({tan}^{\mathrm{2}} \left({x}\right)\right)}{{tan}^{\mathrm{2}} \left({x}\right.}\:{dx}\overset{???} {=}\pi\left(\sqrt{\mathrm{2}}\:−\frac{\pi}{\mathrm{4}}\right) \\ $$$$ \\ $$ Answered…

Let-f-be-defined-in-the-neighborhood-of-x-and-that-f-x-exists-Prove-that-lim-h-0-f-x-h-f-x-h-2f-x-h-2-f-x-

Question Number 62679 by ajfour last updated on 24/Jun/19 $${Let}\:{f}\:{be}\:{defined}\:{in}\:{the}\:{neighborhood} \\ $$$${of}\:{x}\:{and}\:{that}\:{f}\:''\left({x}\right)\:{exists}. \\ $$$${Prove}\:{that}\:\: \\ $$$$\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{f}\left({x}+{h}\right)+{f}\left({x}−{h}\right)−\mathrm{2}{f}\left({x}\right)}{{h}^{\mathrm{2}} }={f}\:''\left({x}\right)\:. \\ $$ Commented by kaivan.ahmadi last updated…

nice-calculus-if-b-gt-a-gt-0-then-prove-a-b-2-gt-b-a-ln-b-ln-a-gt-ab-

Question Number 128005 by mnjuly1970 last updated on 03/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:….{nice}\:\:\:{calculus}… \\ $$$$\:\:{if}\:\:{b}>{a}>\mathrm{0}\:{then}\:{prove}\::: \\ $$$$\:\:\:\:\:\:\:\:\frac{{a}+{b}}{\mathrm{2}}>\:\frac{{b}−{a}}{{ln}\left({b}\right)−{ln}\left({a}\right)}\:>\:\sqrt{{ab}}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:………………………. \\ $$ Answered by mindispower last updated on 06/Jan/21…