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Limits and Derivatives — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSLimits and Derivatives2 Marks
Question
Find 'n' if $\lim\limits_{\text{x} \rightarrow 2}\frac{\text{x}^{\text{n}}-2^{\text{n}}}{\text{x}-2}=80,\text{x}\in\text{N}$
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Answer

Given that $\lim\limits_{\text{x} \rightarrow 2}\frac{\text{x}^{\text{n}}-2^{\text{n}}}{\text{x}-2}=80$
$=\text{n}.(2)^{\text{n}-1}=80$
$=\text{n}\times2^{\text{n}-1}=5\times(2)^{5-1}$
$\therefore\text{n}=5$
Hence, the required answer is n = 5.

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