Find _ x -5 2 [x] . - Vidyadip

Question

Find $\lim\limits_{\text{x}\rightarrow-\frac{5}{2}}{[\text{x}]}.$

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Answer

$\lim\limits_{\text{x}\rightarrow-\frac{5}{2}}{[\text{x}]}$
$\lim\limits_{\text{x}\rightarrow\frac{5}{2}}{[\text{x}]}=\Big[\frac{5}{2}\Big],$
$=[2.5]=2$ [By definition of geatest integer function]
$\Rightarrow\ \lim\limits_{\text{x}\rightarrow\frac{5}{2}}{[\text{x}]}=2$

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