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Question-203305

Question Number 203305 by Ari last updated on 15/Jan/24 Answered by mr W last updated on 15/Jan/24 $${y}={mx}+{c} \\ $$$$\Rightarrow{x}=\frac{{y}}{{m}}−\frac{{c}}{{m}}\:\Rightarrow{f}^{−\mathrm{1}} \left({x}\right)=\frac{{x}}{{m}}−\frac{{c}}{{m}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)={f}\left({x}\right) \\…

Find-lim-x-0-1-cos4x-x-2-

Question Number 203288 by hardmath last updated on 14/Jan/24 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{x}}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}\:−\:\mathrm{cos4x}}{\mathrm{x}^{\mathrm{2}} }\:=\:? \\ $$ Answered by MM42 last updated on 14/Jan/24 $$={lim}_{{x}\rightarrow\mathrm{0}} \:\frac{\mathrm{2}{sin}^{\mathrm{2}} \mathrm{2}{x}}{{x}^{\mathrm{2}} }\:…

f-x-1-x-2-x-if-x-0-2-if-x-0-study-the-continuty-of-f-in-0-

Question Number 203291 by zahaku last updated on 14/Jan/24 $${f}\left({x}\right)=\left\{\mathrm{1}+\frac{\sqrt{{x}^{\mathrm{2}} }}{{x}}\:\:\:{if}\:{x}#\mathrm{0}\right. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}\:\:{if}\:\:{x}=\mathrm{0} \\ $$$${study}\:{the}\:{continuty}\:{of}\:{f}\:{in}\:\mathrm{0} \\ $$ Answered by esmaeil last updated on 15/Jan/24 $${f}\left({x}\right)=\begin{cases}{\mathrm{1}+\frac{\mid{x}\mid}{{x}}\:\:\:\:{if}\:\:{x}\neq\mathrm{0}}\\{\mathrm{2}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:{x}=\mathrm{0}}\end{cases}\:\:\:…

f-x-2ln-x-1-ln-2x-1-1-the-intersextion-Curve-with-axe-XX-2-find-the-equation-of-Circle-tengent-to-the-Curve-f-and-axe-O-Y-Y-gt-0-and-the-relative-maximum-of-f-x-3-the-Area-delimited

Question Number 203260 by a.lgnaoui last updated on 13/Jan/24 $$\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2ln}\mid\mathrm{x}−\mathrm{1}\mid+\mathrm{ln}\left(\mathrm{2x}+\mathrm{1}\right) \\ $$$$\left.\bullet\mathrm{1}\right)−\mathrm{the}\:\mathrm{intersextion}\:\:\mathrm{Curve}\:\mathrm{with} \\ $$$$\mathrm{axe}\:\mathrm{XX}^{'} ? \\ $$$$\left.\bullet\mathrm{2}\right)−\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{Circle}\:\mathrm{tengent}\:\mathrm{to} \\ $$$$\mathrm{the}\:\mathrm{Curve}\:\left(\mathrm{f}\right)\:\mathrm{and}\:\mathrm{axe}\:\left(\mathrm{O},\mathrm{Y}\right):\mathrm{Y}>\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{relative}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right) \\ $$$$\left.\bullet\mathrm{3}\right)−\mathrm{the}\:\mathrm{Area}\:\mathrm{delimited}\:\mathrm{by}\:\mathrm{x}=\mathrm{3} \\ $$$$\:\:\:\:\:\mathrm{max}\:\mathrm{relative}\:\mathrm{and}\:\mathrm{Circle}\:?…

Question-203244

Question Number 203244 by cortano12 last updated on 13/Jan/24 Answered by MathematicalUser2357 last updated on 14/Jan/24 $$\mathrm{If}\:\mathrm{you}\:\mathrm{took}\:\mathrm{that}\:\mathrm{image}\:\mathrm{on}\:\mathrm{FB}, \\ $$$$\mathrm{You}\:\mathrm{will}\:\mathrm{be}\:\mathrm{known}\:\mathrm{soon}. \\ $$$$\mathrm{Here}\:\mathrm{is}\:\mathrm{a}\:\mathrm{proof}: \\ $$ Commented by…

lim-x-0-x-tan-pi-2-1-x-

Question Number 203247 by mathlove last updated on 13/Jan/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:{x}\:{tan}\frac{\pi}{\mathrm{2}}\left(\mathrm{1}+{x}\right)=? \\ $$ Answered by MM42 last updated on 13/Jan/24 $$={lim}_{{x}\rightarrow\mathrm{0}} \:−{xcot}\frac{\pi}{\mathrm{2}}{x}={lim}_{{x}\rightarrow\mathrm{0}} \:−\frac{\frac{\pi}{\mathrm{2}}{xcos}\frac{\pi}{\mathrm{2}}{x}}{{sin}\frac{\pi}{\mathrm{2}}{x}}×\frac{\mathrm{2}}{\pi} \\ $$$$=\:−\frac{\mathrm{2}}{\pi}\:\checkmark…