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Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits3 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
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Answer

$\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{1}{\text{x}+3}-\frac{1}{\text{x}-3}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{\text{x}-3+\text{x}+3}{(\text{x}+3)(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\big(\text{x}^2-9\big)\Big(\frac{2\text{x}}{(\text{x}+3)(\text{x}-3)}\Big)$
$=\lim\limits_{\text{x}\rightarrow3}\frac{(\text{x}-3)(\text{x}+3)(2\text{x})}{(\text{x}+3)(\text{x}-3)}$
$=\lim\limits_{\text{x}\rightarrow3}2(\text{x})=2(3)=6$

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