Question Number 23237 by paro123 last updated on 27/Oct/17
Commented by prakash jain last updated on 28/Oct/17
$$\mathrm{If}\:\mathrm{the}\:\mathrm{function}\:\mathrm{is}\:\mathrm{1}\:\mathrm{everywhere}\:\mathrm{except} \\ $$$$\mathrm{at}\:\mathrm{origin}\:\mathrm{then}\:\mathrm{both}\:\mathrm{repeated}\:\mathrm{amd} \\ $$$$\mathrm{combined}\:\mathrm{limit}\:\mathrm{exists}. \\ $$
Commented by prakash jain last updated on 27/Oct/17
$$\mathrm{The}\:\mathrm{function}\:\mathrm{definition}\:\mathrm{is}\:\mathrm{not}\:\mathrm{complete} \\ $$$$\mathrm{what}\:\mathrm{if}\:{x}=\mathrm{0}\:\mathrm{and}\:{y}\neq\mathrm{0}\:\mathrm{or}\:{y}=\mathrm{0}\:\mathrm{and}\:{x}\neq\mathrm{0}. \\ $$$$\mathrm{please}\:\mathrm{recheck}\:\mathrm{question} \\ $$
Commented by paro123 last updated on 27/Oct/17
$$\mathrm{here}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{0}\:\mathrm{if}\:\:\mathrm{x}=\mathrm{0},\mathrm{y}=\mathrm{0}\:\mathrm{and}\:\mathrm{1}\:\mathrm{otherwise} \\ $$
Commented by prakash jain last updated on 27/Oct/17
$$\mathrm{is}\:\mathrm{this}\:\mathrm{the}\:\mathrm{definition}\:\mathrm{then}? \\ $$$${f}\left({x},{y}\right)=\begin{cases}{\mathrm{0}}&{{x}={y}=\mathrm{0}}\\{\mathrm{1}}&{\mathrm{otherwise}}\end{cases} \\ $$
Commented by paro123 last updated on 28/Oct/17
Commented by paro123 last updated on 28/Oct/17
$$\mathrm{No}.\mathrm{8}.\left(\mathrm{ii}\right) \\ $$