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Limits — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSLimits4 Marks
Question
Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^3+3\text{x}^2+6\text{x}+2}{\text{x}^3+3\text{x}^2-3\text{x}-1}$
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Answer

$\lim\limits_{\text{x}\rightarrow1}\frac{\text{x}^3+3\text{x}^2+6\text{x}+2}{\text{x}^3+3\text{x}^2-3\text{x}-1}$$=\lim\limits_{\text{x}\rightarrow1}\frac{(\text{x}+1)\big(\text{x}^2+4\text{x}-2\big)}{(\text{x}-1)\big(\text{x}^2-4\text{x}+1\big)}$
$=\frac{(1)^24(1)-2}{(1)^24(1)+1}$
$=\frac{1+4-2}{1+4+1}$
$=\frac{3}{6}$
$=\frac{1}{2}$

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