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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits1 Mark
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^3-8}{\text{x}^2-4}$
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Answer

$\lim\limits_{\text{x}\rightarrow2}\frac{\text{x}^3-8}{\text{x}^2-4}$$=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)\big(\text{x}^2+4+2\text{x}\big)}{(\text{x}-2)(\text{x}+2)}$
$=\frac{(2)^2+4+2(2)}{2+2}=\frac{4+4+4}{4}=\frac{12}{4}=3$

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