Category: Relation and Functions

Question Number 145390 by puissant last updated on 04/Jul/21 $$\phi \left(\mathrm{x}\right)=\ln \left(\frac{{\mathrm{e}}^{\mathrm{x}+\cos \left(\mathrm{x}\right)}-\mathrm{e}}{\mathrm{x}+{\mathrm{x}}^2}\right)$$$$\mathrm{montrer}\mathrm{que}\phi \mathrm{se}\mathrm{prolonge}\mathrm{par}\mathrm{continuit}\acute{\mathrm{e}}$$$$\mathrm{en}0.\mathrm{on}\mathrm{note}\psi \mathrm{son}\mathrm{prolongement},\mathrm{montrer}$$$$\mathrm{que}\psi \mathrm{est}\mathrm{d}\acute{\mathrm{e}rivable}\mathrm{en}0..\mathrm{Ainsi}\mathrm{donner}\mathrm{une}$$$$\acute{\mathrm{e}quation}\mathrm{de}\mathrm{la}\mathrm{tangente},\mathrm{position}\mathrm{de}\mathrm{la}\mathrm{courbe}$$$$\mathrm{par}\:\mathrm{rapport}\:\mathrm{a}\:\mathrm{la}\:\mathrm{tangente},\:\mathrm{et}\:\mathrm{faire}\:\mathrm{le}\:\mathrm{dessin}..…

Question Number 79816 by jagoll last updated on 28/Jan/20 $$\mathrm{hello}\mathrm{mister}.$$$$\mathrm{i}\mathrm{need}\mathrm{help}\mathrm{explaining}\mathrm{how}\mathrm{determine}$$$$\mathrm{the}\mathrm{range}\mathrm{of}\mathrm{function}$$$$\mathrm{of}\mathrm{rational}\mathrm{functions}$$$$\mathrm{like}\left(\mathrm{i}\right)\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}}{{\mathrm{px}}^2+\mathrm{qx}+\mathrm{r}}$$$$\left(\mathrm{ii}\right)\mathrm{f}\left(\mathrm{x}\right)=\frac{{\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}}{\mathrm{px}+\mathrm{q}}$$…

Question Number 79756 by mathmax by abdo last updated on 27/Jan/20 $$calculate{lim}_{x\to 1}\frac{sin\left(\pi x\right)}{1-x^2}withouthospitalrule$$ Commented by john santu last updated on 27/Jan/20 $$\underset{{x}\rightarrow\mathrm{1}}…

Question Number 145165 by mathmax by abdo last updated on 02/Jul/21 $$\mathrm{calculate}\sum _{\mathrm{n}=0}^{\mathrm{\infty }}\arctan \left(\frac{2\mathrm{n}+1}{{\mathrm{n}}^4+{2\mathrm{n}}^3+{\mathrm{n}}^2+1}\right)$$ Answered by mnjuly1970 last updated on…

Question Number 145000 by imjagoll last updated on 01/Jul/21 $$\mathrm{If}\mathrm{F}(\mathrm{x}+1)=\mathrm{F}(\mathrm{x}-1)={\mathrm{x}}^2$$$$\mathrm{then}{\mathrm{F}}^{-1}\left(\mathrm{x}\right)=?$$ Commented by prakash jain last updated on 01/Jul/21 $${f}\left({x}+\mathrm{1}\right)={x}^{\mathrm{2}} \Rightarrow{f}\left({x}\right)=\left({x}−\mathrm{1}\right)^{\mathrm{2}}…