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Category: Relation and Functions

Prove-that-f-x-x-2-is-continous-at-x-2-while-f-x-0-x-2-x-2-x-2-is-not-continous-at-x-2-

Question Number 10095 by Tawakalitu ayo mi last updated on 23/Jan/17 $$\mathrm{Prove}\:\mathrm{that}\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:\:\mathrm{is}\:\mathrm{continous}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{while}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\left\{_{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{x}\:=\:\mathrm{2}} ^{\mathrm{x}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{x}\:\neq\:\mathrm{2}} \:\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{continous}\:\mathrm{at}\:\mathrm{x}\:=\:\mathrm{2}\right. \\ $$ Answered by sandy_suhendra last updated…

Question-9960

Question Number 9960 by Tawakalitu ayo mi last updated on 19/Jan/17 Answered by sandy_suhendra last updated on 20/Jan/17 $$\left(\mathrm{i}\right)\:\mathrm{f}\left(−\mathrm{1}\right)=\left(−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}\left(−\mathrm{1}\right)−\mathrm{1}=−\mathrm{3} \\ $$$$\:\:\:\:\:\:\mathrm{li}\underset{\mathrm{x}\rightarrow−\mathrm{1}} {\mathrm{m}}\:\mathrm{x}^{\mathrm{2}} +\mathrm{3x}−\mathrm{1}=−\mathrm{3} \\…

Question-140748

Question Number 140748 by 676597498 last updated on 12/May/21 Answered by qaz last updated on 12/May/21 $$\left({i}\right)…{r}=\frac{\mathrm{2}}{\mathrm{1}+\mathrm{sin}\:\theta} \\ $$$$\Rightarrow{r}+{r}\mathrm{sin}\:\theta=\mathrm{2} \\ $$$$\Rightarrow\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }+{y}=\mathrm{2} \\ $$$$\Rightarrow{x}^{\mathrm{2}}…