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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits3 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{2}{\text{x}^2-4\text{x}+3}\Big)$
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Answer

$\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{2}{\text{x}^2-4\text{x}+3}\Big)$ $=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{1}{\text{x}-3}-\frac{2}{(\text{x}-3)(\text{x}-1)}\Big)$ $=\lim\limits_{\text{x}\rightarrow3}\Big(\frac{\text{x}-1-2}{(\text{x}-1)(\text{x}-3)}\Big)$ $=\lim\limits_{\text{x}\rightarrow3}\bigg(\frac{\text{x}-3}{(\text{x}-1)(\text{x}-3)}\bigg)$ $=\lim\limits_{\text{x}\rightarrow3}\frac{1}{\text{x}-1}$ $=\frac{1}{3-1}$ $=\frac12$

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