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Limits — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits2 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow-\frac12}\frac{8\text{x}^3+1}{2{\text{x}}+1}$
✓

Answer

$\lim\limits_{\text{x}\rightarrow-\frac12}\frac{8\text{x}^3+1}{2{\text{x}}+1}=\lim\limits_{\text{x}\rightarrow-\frac12}\frac{8\Big(\text{x}^2+\frac18\Big)}{2\Big(\text{x}+\frac12\Big)}$
$=\frac82\lim\limits_{\text{x}\rightarrow-\frac12}\frac{\Big(\text{x}^3+\big(\frac12\big)^3\Big)}{\text{x}+\frac12}$
$=4\lim\limits_{\text{x}\rightarrow-\frac{1}{2}}\frac{\Big(\text{x}+\frac12\Big)\Big(\text{x}^2+\frac14-\frac12\text{x}\Big)}{\Big(\text{x}+\frac12\Big)}$
$=4\Big(\Big(\frac{-1}{2}\Big)+\frac14-\frac12\Big(\frac{-1}{2}\Big)\Big)$
$=4\Big(\frac14+\frac14+\frac14\Big)$
$=3$

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