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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
Find $\lim\limits_{\text{x}\rightarrow3^+}\frac{\text{x}}{[\text{x}]}.$ is it equal to $\lim\limits_{\text{x}\rightarrow3^-}\frac{\text{x}}{[\text{x}]}.$
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Answer

$\lim\limits_{\text{x}\rightarrow3^+}\frac{\text{x}}{[\text{x}]}=\lim\limits_{\text{x}\rightarrow3^+}\frac{\text{x}}{3}=\frac{3}{3}=1$ $\lim\limits_{\text{x}\rightarrow3^-}\frac{\text{x}}{[\text{x}]}=\lim\limits_{\text{x}\rightarrow3^-}\frac{\text{x}}{2}=\frac{3}{2}=1.5$ $\therefore\ \lim\limits_{\text{x}\rightarrow3^+}\frac{\text{x}}{[\text{x}]}\ne\lim\limits_{\text{x}\rightarrow3^-}\frac{\text{x}}{[\text{x}]}$

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