Question Number 199312 by Mastermind last updated on 01/Nov/23
$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{continuity}\:\mathrm{ortherwise}\:\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{following}\:\mathrm{functions} \\ $$$$ \\ $$$$\left.\mathrm{a}\right)\:\frac{\mathrm{7x}^{\mathrm{2}} +\mathrm{x}−\mathrm{3}}{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.\mathrm{b}\right)\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{1} \\ $$$$ \\ $$$$\left.\mathrm{c}\right)\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left\{_{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:,\:\:\:\:\:\mathrm{x}=\mathrm{1}} ^{\frac{\mathrm{4}−\mathrm{x}^{\mathrm{2}} }{\mathrm{3}−\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{5}}}\:\:\:\:\:\:,\:\:\:\:\mathrm{x}\neq\mathrm{2}} \right. \\ $$
Answered by AST last updated on 01/Nov/23
$$\left.{a}\right){Not}\:{continuous}\:{at}\:{x}=\mathrm{2}\: \\ $$$$\left.{b}\right){Continuous} \\ $$$$\left.{c}\right)\:{Not}\:{continuous}\:{at}\:{x}=\sqrt{\mathrm{14}} \\ $$$$ \\ $$
Commented by Mastermind last updated on 01/Nov/23
$$\mathrm{I}\:\mathrm{need}\:\mathrm{full}\:\mathrm{detailed}\:\mathrm{explanation}/\mathrm{solution} \\ $$$$\mathrm{on}\:\mathrm{it}= \\ $$$$\mathrm{thank}\:\mathrm{you} \\ $$
Commented by AST last updated on 01/Nov/23
$$\left.{a}\right){f}\left(\mathrm{2}\right)\:{has}\:{no}\:{output} \\ $$$$\left.{b}\right){All}\:{polynomial}\:{functions}\:{are}\:{continuous} \\ $$$$\left.{c}\right){f}\left(\sqrt{\mathrm{14}}\right)\:{has}\:{no}\:{output} \\ $$
Commented by Mastermind last updated on 01/Nov/23
$$\mathrm{Thank}\:\mathrm{you} \\ $$