Question Number 135216 by mohammad17 last updated on 11/Mar/21
![lim_(x→3^+ ) (([x]^2 −9)/(x−3))](https://www.tinkutara.com/question/Q135216.png)
$${lim}_{{x}\rightarrow\mathrm{3}^{+} } \frac{\left[{x}\right]^{\mathrm{2}} −\mathrm{9}}{{x}−\mathrm{3}} \\ $$
Answered by Olaf last updated on 11/Mar/21
![lim_(x→3^+ ) (([x]^2 −9)/(x−3)) = lim_(h→0^+ ) (([3+h]^2 −9)/(3+h−3)) = lim_(h→0^+ ) (0^+ /h) = +∞](https://www.tinkutara.com/question/Q135235.png)
$$\underset{{x}\rightarrow\mathrm{3}^{+} } {\mathrm{lim}}\:\frac{\left[{x}\right]^{\mathrm{2}} −\mathrm{9}}{{x}−\mathrm{3}}\:=\:\underset{{h}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\left[\mathrm{3}+{h}\right]^{\mathrm{2}} −\mathrm{9}}{\mathrm{3}+{h}−\mathrm{3}}\:=\:\underset{{h}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\:\frac{\mathrm{0}^{+} }{{h}}\:=\:+\infty \\ $$