Limits and Derivatives — Maths STD 11 Science — Question
CBSE 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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