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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits2 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow2}\Big(\frac{1}{\text{x}-2}-\frac{4}{\text{x}^3-2\text{x}^2}\Big)$
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Answer

$\lim\limits_{\text{x}\rightarrow2}\Big(\frac{1}{\text{x}-2}-\frac{4}{\text{x}^3-2\text{x}^2}\Big)$ $=\lim\limits_{\text{x}\rightarrow2}\Big(\frac{1}{​​​​\text{x}-2}-\frac{4}{\text{x}^2(\text{x}-2)}\Big)$ $=\lim\limits_{\text{x}\rightarrow2}\Big(\frac{\text{x}^2-4}{\text{x}^2(\text{x}-2)}\Big)$ $=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}-2)(\text{x}+2)}{\text{x}^2(\text{x}-2)}$ $=\lim\limits_{\text{x}\rightarrow2}\frac{(\text{x}+2)}{\text{x}^2}$ $=\frac{(2+2)}{2^2}=\frac{4}{4}$ $=1$

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