Category: Relation and Functions

Question Number 59186 by maxmathsup by imad last updated on 05/May/19 $$calculate{lim}_{x\to 0}\frac{arctan\left\{ln(1+x)\right\}}{x^2}$$ Commented by kaivan.ahmadi last updated on 05/May/19 $${hop} \…

Question Number 59182 by maxmathsup by imad last updated on 05/May/19 $$letf\left(x\right)=arctan(1+ix)$$$$determineRe\left(f\left(x\right)\right)andIm\left(f\left(x\right)\right)dx$$ Commented by maxmathsup by imad last updated on 10/Jun/19…

Question Number 124444 by benjo_mathlover last updated on 03/Dec/20 $$Iff\left(\frac{2}{x}\right)=\frac{3}{2+4x}and{f}^{-1}\left(p\right)=2$$$$thenp=?$$ Answered by bemath last updated on 03/Dec/20 $$\:\Leftrightarrow\:{f}^{−\mathrm{1}} \left({p}\right)=\mathrm{2}\:{then}\:{f}\left(\mathrm{2}\right)={p} \…

Question Number 124102 by mnjuly1970 last updated on 30/Nov/20 $$\dots advancedcalculus\dots$$$$p,qarepositiveintegersand$$$$p⩾q:let:\varphi (p,q)={\int }_0^1{x}^p{\left\{\frac{1}{x}\right\}}^{q}dx$$$$provethat::$$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\phi\left({n},{n}\right)\overset{?} {=}\mathrm{1}−\frac{\mathrm{1}}{{n}+\mathrm{1}}\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\zeta\left({k}+\mathrm{1}\right)…

Question Number 124066 by Bird last updated on 30/Nov/20 $$letf\left(x\right)=arctan\left(\frac{2}{x}\right)$$$$calculate{f}^{\left(n\right)}\left(x\right)and{f}^{\left(n\right)}\left(1\right)$$$$find{f}^{\left(7\right)}\left(\frac{1}{7}\right)$$ Answered by Olaf last updated on…