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Question Number 112370 by Eric002 last updated on 07/Sep/20
lim_(x→0^+ ) ((x−⌊x⌋)/x^2 )  ⌊x⌋ is floor function
$$\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\frac{{x}−\lfloor{x}\rfloor}{{x}^{\mathrm{2}} } \\ $$$$\lfloor{x}\rfloor\:{is}\:{floor}\:{function} \\ $$
Commented by kaivan.ahmadi last updated on 07/Sep/20
⌊0^+ ⌋=0  ⇒lim_(x→^+ )  (x/x^2 )=lim_(x→0^+ ) (1/x)=+∞
$$\lfloor\mathrm{0}^{+} \rfloor=\mathrm{0} \\ $$$$\Rightarrow{lim}_{{x}\rightarrow^{+} } \:\frac{{x}}{{x}^{\mathrm{2}} }={lim}_{{x}\rightarrow\mathrm{0}^{+} } \frac{\mathrm{1}}{{x}}=+\infty \\ $$$$ \\ $$

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