Question Number 25279 by NECx last updated on 07/Dec/17 $${Find}\:{the}\:{domain}\:{and}\:{range}\:{of} \\ $$$${f}\left({x}\right)=\sqrt{\left(\frac{{x}−\mathrm{5}}{{x}−\mathrm{3}}\right)} \\ $$ Answered by SAGARSTARK last updated on 07/Dec/17 $$\left(\frac{{x}−\mathrm{5}}{{x}−\mathrm{3}}\right)\geqslant\mathrm{0}\:\boldsymbol{\mathrm{x}}\in\left(−\infty,\mathrm{3}\right)\cup\left[\mathrm{5},\infty\right)\:{using}\: \\ $$$${wavy}\:{curve}\:{method} \\…
Question Number 25280 by NECx last updated on 07/Dec/17 $${Find}\:{the}\:{limit}\:{off}\left({x}\right)\underset{{x}\rightarrow\mathrm{4}} {\:}=\left(\frac{{x}+\mathrm{2}}{{x}^{\mathrm{2}} −\mathrm{4}}\right) \\ $$ Answered by Rasheed.Sindhi last updated on 07/Dec/17 $$\mathrm{Since}\:\mathrm{limit}\:\mathrm{of}\:\mathrm{the}\:\mathrm{denominator}\neq\mathrm{0} \\ $$$$\mathrm{So} \\…
Question Number 25251 by NECx last updated on 07/Dec/17 $${state}\:{the}\:{domain}\:{and}\:{range}\:{in}\: \\ $$$${intervals}\:{for}\:{the}\:{following}\:{when} \\ $$$${they}\:{are}\:{said}\:{the}\:{be}\:{continuous}\:{at} \\ $$$${a}\:{point}: \\ $$$$\left.{a}\right){a}\:{polynomial}\:{function} \\ $$$$\left.{b}\right){a}\:{rational}\:{function} \\ $$$$\left.{c}\right){an}\:{absolute}\:{value}\:{function} \\ $$$$\left.{d}\right){a}\:{trig}\:{function} \\…
Question Number 90750 by abdomathmax last updated on 25/Apr/20 $${let}\:\:\alpha\:{and}\:\beta\:{roots}\:{of}\:\:{x}^{\mathrm{2}} −{x}+\mathrm{2}=\mathrm{0}\:\:{calculate} \\ $$$${A}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:\left(\alpha^{{k}} \:+\beta^{{k}} \right) \\ $$$${B}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(\alpha^{{k}} −\beta^{{k}} \right)…
Question Number 90751 by abdomathmax last updated on 25/Apr/20 $$\:{calculste}\:{lim}_{{n}\rightarrow\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\sum_{{k}=\mathrm{1}} ^{{n}} \:{karctan}\left(\frac{{k}}{{n}}\right) \\ $$ Commented by mathmax by abdo last updated on 26/Apr/20…
Question Number 90749 by abdomathmax last updated on 25/Apr/20 $${find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}\left(\frac{{k}\pi}{{n}}\right) \\ $$ Commented by mathmax by abdo last updated on 26/Apr/20…
Question Number 90743 by abdomathmax last updated on 25/Apr/20 $${find}\:{nature}\:{of}\:{the}\:{serie}\:\Sigma\:\left(−\mathrm{1}\right)^{{n}} \:{U}_{{n}} \\ $$$${with}\:\:{U}_{{n}+\mathrm{1}} =\frac{{e}^{−{U}_{{n}} } }{{n}+\mathrm{1}}\:\:\:\:\:\left({U}_{\mathrm{0}} =\mathrm{1}\right) \\ $$ Answered by ~blr237~ last updated on…
Question Number 90564 by mathmax by abdo last updated on 24/Apr/20 $${find}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\frac{\left(^{\mathrm{3}} \sqrt{\mathrm{1}+{cos}\left(\mathrm{2}{x}\right)}−\left(^{\mathrm{3}} \sqrt{\mathrm{2}}\right)\right.}{{x}^{\mathrm{2}} {sin}\left(\mathrm{3}{x}\right)} \\ $$ Commented by jagoll last updated on 25/Apr/20…
Question Number 24981 by tawa tawa last updated on 30/Nov/17 Commented by tawa tawa last updated on 30/Nov/17 $$\mathrm{please}\:\mathrm{help}. \\ $$ Answered by kaivan.ahmadi last…
Question Number 90287 by jagoll last updated on 22/Apr/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{6}\:,\:\mathrm{x}\geqslant\mathrm{1}}\\{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{2}\:,\mathrm{x}<\mathrm{1}}\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{c}\:\in\:\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{c}\right)\:=\:\mathrm{4} \\ $$ Answered by MJS last updated on…