Question Number 214251 by Hanuda354 last updated on 02/Dec/24 Commented by Hanuda354 last updated on 02/Dec/24 $$\mathrm{Determine}\:\:\mathrm{where}\:\:{f}\:\:\mathrm{is}\:\:\mathrm{continuous}\:\:\mathrm{algebraically}. \\ $$$$\mathrm{Write}\:\:\mathrm{in}\:\:\mathrm{interval}\:\:\mathrm{notation}. \\ $$ Answered by a.lgnaoui last…
Question Number 214256 by Einstein2006 last updated on 02/Dec/24 $$\boldsymbol{{lim}}_{\boldsymbol{{x}}\:\rightarrow\:\mathrm{1}} \propto.\boldsymbol{{arctan}}\left(\frac{\mathrm{2}}{\mathrm{1}\:+\boldsymbol{{x}}}\:−\:\mathrm{1}\right) \\ $$$$\bullet\:\boldsymbol{{Calculons}}\:\boldsymbol{{la}}\:\boldsymbol{{limite}}\:\boldsymbol{{a}}\:\boldsymbol{{l}}'\boldsymbol{{intrieur}}: \\ $$$$\frac{\mathrm{2}}{\mathrm{1}\:+\:\boldsymbol{{x}}}\:−\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{x}}\:\rightarrow\:\mathrm{1}} {arctan}\left(\frac{\mathrm{2}}{\mathrm{1}\:+\:{x}}\:−\:\mathrm{1}\right)=\:\boldsymbol{{arctan}}\left(\mathrm{0}\right)\:=\:\mathrm{0} \\ $$$$\: \\ $$$$\boldsymbol{{lim}}_{\boldsymbol{{x}}\rightarrow\mathrm{1}} \propto.{arctan}\left(\frac{\mathrm{2}}{\mathrm{1}+\:{x}}\:−\:\mathrm{1}\right)\:=\propto.\mathrm{0}\:…
Question Number 214205 by MathematicalUser2357 last updated on 01/Dec/24 $${f}\left({x}+\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}\right)={x}−\sqrt{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${f}\left(\mathrm{2}\right)+{f}\left(\mathrm{3}\right)+{f}\left(\mathrm{6}\right)=? \\ $$ Answered by golsendro last updated on 01/Dec/24 $$\:\:\:\:\underline{\underbrace{\:}} \underline{…
Question Number 214152 by Ismoiljon_008 last updated on 29/Nov/24 Commented by Ismoiljon_008 last updated on 29/Nov/24 $$ \\ $$$$\:\:\:{What}\:{is}\:{the}\:{number}\:{of}\:{points}\:{in}\:{the}\: \\ $$$$\:\:\:{interval}\:\left(−\mathrm{1};\mathrm{12}\right)\:{where}\:{the}\:{derivative} \\ $$$$\:\:\:{of}\:{the}\:{function}\:{y}\:=\:{f}\left({x}\right)\:{is}\:{equal}\:{to}\:{zero}\:? \\ $$…
Question Number 214140 by issac last updated on 29/Nov/24 $$\mathrm{Let}\:{F}\:;\:\mathbb{R}^{{n}} \rightarrow\mathbb{R}^{{n}} \:\mathrm{be}\:\mathrm{continuously} \\ $$$$\mathrm{differentiable}\: \\ $$$$\left.\boldsymbol{\mathrm{a}}\right)\:\mathrm{assume}\:\mathrm{that}\:\mathrm{the}\:\mathrm{Jacoboian}\:\mathrm{matrix}\: \\ $$$$\frac{\partial{f}_{{i}} }{\partial{x}_{{j}} }\:\mathrm{has}\:\mathrm{rank}\:{n}\:\mathrm{everywhere} \\ $$$$\mathrm{prove}\:\mathrm{that}\:{f}\left(\mathbb{R}^{{n}} \right)\mathrm{is}\:\mathrm{open} \\ $$$$\left.\boldsymbol{\mathrm{b}}\right)\:\mathrm{suppose}\:\mathrm{that}\:{f}^{−\mathrm{1}}…
Question Number 214138 by abdelsalam last updated on 29/Nov/24 Commented by abdelsalam last updated on 29/Nov/24 $${find}\:\:{x} \\ $$ Answered by issac last updated on…
Question Number 214163 by issac last updated on 29/Nov/24 Commented by mathkun last updated on 30/Nov/24 $$\mathrm{I}\:\mathrm{am}\:\mathrm{a}\:\mathrm{begginer}\:\mathrm{in}\:\mathrm{Calculus}. \\ $$$$\mathrm{How}\:\mathrm{do}\:\mathrm{you}\:\mathrm{find}\:\mathrm{the}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{this}\:\mathrm{function}? \\ $$$$\mathrm{The}\:\mathrm{equation}\:\mathrm{for}\:\mathrm{y}\:\mathrm{with}\:\mathrm{respect}\:\mathrm{to}\:\mathrm{x}\:\mathrm{is}\:\mathrm{not}\:\mathrm{given}. \\ $$ Commented by…
Question Number 214111 by issac last updated on 28/Nov/24 $$\mathrm{hmmmm}………… \\ $$$$\mathrm{can}\:\mathrm{we}\:\mathrm{find}\:\mathrm{closed}\:\mathrm{form}\:\mathrm{of}\:\mathrm{sum} \\ $$$$\underset{{j}=\mathrm{0}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}^{{j}} } }\:??\:\mathrm{or}\:\mathrm{any}\:\mathrm{idea}..? \\ $$ Terms of Service Privacy Policy…
Question Number 214116 by Ayya last updated on 28/Nov/24 $${f}\left({x}\right)=\frac{\mathrm{3}{x}−\mathrm{5}}{{x}^{\mathrm{2}} } \\ $$ Answered by issac last updated on 28/Nov/24 $$\underset{{z}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{\mathrm{3}{z}−\mathrm{5}}{{z}^{\mathrm{2}} }=\mathrm{div} \\ $$$$\underset{{z}\rightarrow\pm\infty}…
Question Number 214091 by 2AR last updated on 27/Nov/24 Answered by A5T last updated on 27/Nov/24 $$?=\left(\mathrm{256}^{\mathrm{256}} \right)^{\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{11}} }} =\left(\mathrm{2}^{\mathrm{8}} \right)^{\frac{\mathrm{2}^{\mathrm{8}} }{\mathrm{2}^{\mathrm{11}} }} =\left(\mathrm{2}^{\mathrm{8}} \right)^{\mathrm{2}^{−\mathrm{3}}…