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Question Number 181749 by Shrinava last updated on 29/Nov/22

Answered by Frix last updated on 30/Nov/22

$$\mathrm{A}\mathrm{function}f\left(x\right)\mathrm{is}\mathrm{continuous}\mathrm{in}(a,b)\mathrm{if}$$$$\mathrm{\forall }c\in (a,b)$$$$1.f\left(c\right)\mathrm{is}\mathrm{defined}\left[\mathrm{it}\mathrm{has}\mathrm{no}\mathrm{gaps}\right]$$$$2.\underset{x\to c}{\lim }f\left(x\right)=f\left(c\right)[\mathrm{it}{\mathrm{doesn}}^{\prime }\mathrm{t}‘‘{\mathrm{jump}}^{″}]$$$$\Rightarrow f\left(x\right)=\sqrt[3]{x}\mathrm{is}\mathrm{continuous}\mathrm{in}(-\mathrm{\infty },+\mathrm{\infty })$$

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