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Limits — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsLimits4 Marks
Question
Evaluate the following limit:
$\lim\limits_{\text{n}\rightarrow\infty}\frac{\text{x}^4+7\text{x}^3+46\text{x}+\text{a}}{\text{x}^4+6},$ where a is a non-zero real number.
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Answer

$\lim\limits_{\text{n}\rightarrow\infty}\frac{\text{x}^4+7\text{x}^3+46\text{x}+\text{a}}{\text{x}^4+6}$ $\Big[\frac{\infty}{\infty}​\text{ from}\Big]$
$=\lim\limits_{\text{n}\rightarrow\infty}\frac{1+\frac{7}{\text{x}}+\frac{46}{\text{x}^3}+\frac{\text{a}}{\text{x}^4}}{1+\frac{6}{\text{x}^4}}$
$=1$

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